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  • 1.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Bordemann, Martin
    Hofer, Laurent
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Shimada, Hidehiko
    Fuzzy Riemann surfaces2009Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, nr 6, s. 047-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C (onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

  • 2.
    Arnlind, Joakim
    et al.
    Inst Hautes Etud Sci.
    Bordemann, Martin
    Univ Haute Alsace, Lab MIA.
    Hofer, Laurent
    Univ Luxembourg.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Shimada, Hidehiko
    Max Planck Inst Gravitat Phys.
    Noncommutative Riemann Surfaces by Embeddings in R-32009Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 288, nr 2, s. 403-429Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce C-Algebras of compact Riemann surfaces ∑ as non-commutative analogues of the Poisson algebra of smooth functions on ∑. Representations of these algebrasgive rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.

  • 3. Arnlind, Joakim
    et al.
    Bordemann, Martin
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lee, Choonkyu
    Goldfish geodesics and hamiltonian reduction of matrix dynamics2008Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 84, nr 1, s. 89-98Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe the Hamiltonian reduction of a time-dependent real-symmetric NxN matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars-Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

  • 4. Arnlind, Joakim
    et al.
    Choe, Jaigyoung
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Noncommutative Minimal Surfaces2016Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, nr 8, s. 1109-1129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 5.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Discrete minimal surface algebras2010Inngår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 6, s. Paper 042,18-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl(n) (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d <= 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is ( generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  • 6.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Eigenvalue dynamics, Follytons and large N limits of matrices2006Inngår i: Applications of Random Matrices in Physics / [ed] Brezin, E; Kazakov, V; Serban, D; Wiegmann, P; Zabrodin, A, DORDRECHT: SPRINGER , 2006, Vol. 221, s. 89-94Konferansepaper (Fagfellevurdert)
    Abstract [en]

    How do the eigenvalues of a “free” hermitian N × N matrix X(t) evolve in time? The answer is provided by the rational Calogero-Moser systems [5, 13] if (!) the initial conditions are chosen such that i[X(0),Ẋ(0)] has a non-zero eigenvalue of multiplicity N–1; for generic X(0),Ẋ(0) the question remained unanswered for 30 years.

  • 7.
    Arnlind, Joakim
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Hoppe, Jens
    KTH, Tidigare Institutioner, Matematik.
    Eigenvalue Dynamics off the Calogero-Moser system2004Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, nr 2, s. 121-129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.

  • 8. Arnlind, Joakim
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Sogang University, South Korea .
    The world as quantized minimal surfaces2013Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 723, nr 4-5, s. 397-400Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is pointed out that the equations Sigma(d)(i=1)[X-i, [X-i, X-j]] = 0 (and its super-symmetrizations, playing a central role in M-theory matrix models) describe non-commutative minimal surfaces - and can be solved as such.

  • 9.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Huisken, Gerhard
    Max Planck Institute for Gravitational Physics.
    Multi linear formulation of differential geometry and matrix regularizations2012Inngår i: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 91, nr 1, s. 1-39Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that many aspects of the differential geometry of em-bedded Riemannian manifolds can be formulated in terms of multilinear algebraic structures on the space of smooth functions. Inparticular, we find algebraic expressions for Weingarten’s formula,the Ricci curvature and the Codazzi-Mainardi equations.For matrix analogues of embedded surfaces we define discretecurvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressionsfor the discrete Gauss curvature in terms of matrices representingthe embedding coordinates, and explicit examples are provided.Furthermore, we illustrate the fact that techniques from differen-tial geometry can carry over to matrix analogues by proving thata bound on the discrete Gauss curvature implies a bound on theeigenvalues of the discrete Laplace operator.

  • 10.
    Arnlind, Joakim
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Hoppe, Jens
    KTH, Tidigare Institutioner, Matematik.
    Theisen, Stefan
    Albert Einstein Inst.
    Spinning Membranes2004Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, nr 1-2, s. 118-128Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdS(p) X S-q, as well as in flat space-time. Nontrivial reductions of the BMN matrix model equations are also given.

  • 11.
    Atai, Farrokh
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hynek, Mariusz
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Variational orthogonalizationManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.

  • 12.
    Bach, Volker
    et al.
    Mainz University, Department of Mathematics.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Dynamical Symmetries in Supersymmetric Matrix2008Inngår i: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 13, s. 103-116Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).

  • 13. Bachas, Constantin
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Pioline, Boris
    Nahm's equations, {$\scr N=1^*$} domain walls, and {D}-strings in {${\rm AdS}_5\times S_5$}2001Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, nr 7, s. Paper 41,28-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the following two problems: classical domain walls in the = 1* mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS5 correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.

  • 14.
    Bellettini, Giovanni
    et al.
    Dipartimento di Matematica, Università di Roma Tor Vergata.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Novaga, Matteo
    Dipartimento di Matematica Pura e Applicata, Università di Padova.
    Orlandi, Giandomenico
    Dipartimento di Informatica, Università di Verona.
    Closure and Convexity Results for Closed Relativistic Strings2010Inngår i: Complex Analysis and Operator Theory, ISSN 1661-8254, Vol. 4, nr 3, s. 473-496Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study various properties of closed relativistic strings. In particular, we characterize their closure under uniform convergence, extending a previous result by Y. Brenier on graph-like unbounded strings, and we discuss some related examples. Then we study the collapsing profile of uniformly convex planar strings which start with zero initial velocity, and we obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves. We conclude the paper with the discussion of an example of weak Lipschitz evolution starting from the square in the plane.

  • 15.
    Choe, Jaigyoung
    et al.
    Korea Inst Adv Study, Seoul 02455, South Korea..
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Higher dimensional Schwarz's surfaces and Scherk's surfaces2018Inngår i: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 57, nr 4, artikkel-id 107Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Higher dimensional generalizations of Schwarz's P-surface, Schwarz's D-surface and Scherk's second surface are constructed as complete embedded periodic minimal hypersurfaces in R-n.

  • 16.
    de Woul, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge2011Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, nr 1, s. 031-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.

  • 17.
    de Woul, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
    Sundin, Martin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    A dynamical symmetry for supermembranes2011Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 3, nr 134Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A dynamical symmetry for supersymmetric extended objects is given.

  • 18. Eggers, J.
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Singularity formation for time-like extremal hypersurfaces2009Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 680, nr 3, s. 274-278Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive self-similar string solutions in a graph representation, near the point of singularity formation, which can be shown to extend to point-like singularities on M(em)branes, as well as to the radially symmetric case. Crown

  • 19. Eggers, Jens
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.). KIAS and Sogang University, Korea.
    Hynek, Mariusz
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Suramlishvili, Nugzar
    Singularities of relativistic membranes2015Inngår i: Geometric Flows, ISSN 2353-3382, Vol. 1, nr 1Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R3,1.

  • 20. Fredenhagen, Stefan
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hynek, Mariusz
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    The Lorentz anomaly via operator product expansion2015Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, nr 10, artikkel-id 102302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than forty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.

  • 21. Frohlich J,
    et al.
    Graf GM,
    Hasler D,
    Hoppe, Jens
    KTH, Tidigare Institutioner                               , Matematik.
    Yau ST,
    Asymptotic form of zero energy wave functions in supersymmetric matrix models2000Inngår i: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 567, nr 1-2, s. 231-248Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive the power law decay, and asymptotic form, of SU(2) X Spin(d) invariant wavefunctions satisfying Q(beta)psi=0 for all s(d) = 2(d - 1) supercharges of reduced (d + 1)-dimensional supersymmetric SU(2) Yang-Mills theory, of, respectively, the SU(2) matrix model related to supermembranes in d + 2 dimensions.

  • 22. Graf, G. M.
    et al.
    Hasler, D.
    Hoppe, Jens
    No zero energy states for the supersymmetric x(2)y(2) potential2002Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 60, nr 2, s. 191-196Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the positive supersymmetric matrix-valued differential operator H = p(x)(2) + p(y)(2) + x(2)y(2) + xsigma(3) + ysigma(1) has no zero modes, i.e., Hpsi = 0 implies psi = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang Mills theories.

  • 23.
    Hoppe, Jens
    KTH, Tidigare Institutioner                               , Matematik.
    Asymptotic form of zero energy wave functions in supersymmetric matrix models2000Inngår i: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 48, nr 1-3, s. 129-131Konferansepaper (Fagfellevurdert)
  • 24.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Curved space (matrix) membranes2011Inngår i: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 43, nr 9, s. 2523-2526Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hamiltonian formulations of M-branes moving in curved backgrounds are given.

  • 25.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Fundamental structures of M(brane) theory2011Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 695, nr 1-4, s. 384-386Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A dynamical symmetry, as well as special diffeomorphism algebras generalizing the Witt-Virasoro algebra, related to Poincare invariance and crucial with regard to quantization, questions of integrability, and M(atrix) theory, are found to exist in the theory of relativistic extended objects of any dimension.

  • 26.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Geodesics on ellipsoids2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Various ways of describing geodesic motion on Ellipsoids are presented (intrinsic and constrained formulations) including Jacobi’s solution, Weierstrass’ solution, and level set Liouville integrability.

  • 27.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Matrix models and Lorentz invariance2011Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 44, nr 5, s. 055402-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The question of Lorentz invariance in the membrane matrix model is addressed.

  • 28.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Quantum Reconstruction AlgebrasManuskript (preprint) (Annet vitenskapelig)
  • 29.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Reformulating M-brane equations2008Inngår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 663, nr 4, s. 351-352Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A Lorentz invariant formulation of Born-Infeld M-brane equations that are not diffeomorphism invariant is presented, and their relation to the standard "extremal-volume" equations clarified.

  • 30.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Relativistic membranes2013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 2, s. 023001-Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    The classical dynamics of M-dimensional extended objects arising from stationary points of the world volume swept out in space time is discussed from various points of view. An introduction to the Hamiltonian mechanics of bosonic compact M(em)branes is given, emphasing the diversity of the different formulations and gauge choices. For moving hypersurfaces, a graph description-including its nonlinear realization of Lorentz invariance-and hydrodynamic formulations (in light-cone coordinates as well as when choosing the time coordinate of a Lorentz observer as the dependent variable) are presented. A matrix regularization for M = 2 (existing for all topologies) is explained in detail for the 2-sphere, as well as multilinear formulations for M > 2. The recently found dynamical symmetry that exists for all M and related reconstruction algebras are covered, just as some explicit solutions of the level-set equations.

  • 31.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    U(1) Invariant Membranes and Singularities2009Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A formulation of U(1)-symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE's, as well as some ideas concerning singularities and integrability.

  • 32.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Korea Inst Adv Study, South Korea.
    Hynek, Mariusz
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Diffeomorphism algebra structure and membrane theory2012Inngår i: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 2, nr 3, s. 277-283Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Explicit structure constants are calculated for Lie algebras of vectorfields on 2-dimensional compact manifolds.

  • 33.
    Hoppe, Jens
    et al.
    KTH, Tidigare Institutioner                               , Matematik.
    Kazakov, V,
    Kostov, I.K.
    Dimensionally reduced SYM4 as solvable matrix quantum mechanics2000Inngår i: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 571, nr 1-2, s. 479-509Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the quantum mechanical model obtained as a dimensional reduction of N = 1 super Yang-Mills theory to a periodic light cone "time''. After mapping the theory to a cohomological field theory, the partition function (with periodic boundary conditions) regularized by a massive term appears to be equal to the partition function of the twisted matrix oscillator. We show that this partition function perturbed by the operator of the holonomy around the time circle is a tau function of Toda hierarchy. We solve the model in the large N limit and study the universal properties of the solution in the scaling limit of vanishing perturbation. We find in this limit a phase transition of Gross-Witten type.

  • 34.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Laptev, Ari
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ostensson, J.
    Solitons and the removal of eigenvalues for fourth-order differential operators2006Inngår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A nonlinear functional Q[u, v] is given that governs the loss, respectively gain, of ( doubly degenerate) eigenvalues of fourth-order differential operators L = partial derivative(4) + partial derivative u partial derivative + v on the line. Apart from factorizing L as A*A + E-0, providing several explicit examples, and deriving various relations between u, v, and the eigenfunctions of L, we find u and v such that L is isospectral to the free operator L-0 = partial derivative(4) up to one (multiplicity 2) eigenvalue E-0 < 0. Not unexpectedly, this choice of u, v leads to exact solutions of the corresponding time-dependent PDE's. Removal of eigenvalues allows us to obtain a sharp Lieb-Thirring inequality for a class of operators L whose negative eigenvalues are of multiplicity two.

  • 35.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lee, Ki-Myeong
    New BPS configurations of BMN matrix theory2008Inngår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, nr 6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We explore the 1/2 BPS configurations in BMN matrix theory with SO(3) angular momentum of SO(3) x SO(6) symmetry. The fluctuation analysis of the BPS configurations near the abelian solutions and also the fuzzy two sphere vacua reveals how nonabelian BPS configurations emerge. Especially the irreducible nonabelian configurations seem to have the maximal angular momentum of order N-3 ,beyond which they collapse to abelian ones. We also find some new BPS configurations explicitly.

  • 36.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Linardopoulos, Georgios
    Turgut, O. Teoman
    New minimal hypersurfaces in R(k+1)(2k+1) and S2k2+3k2017Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, nr 17-18, s. 2874-2878Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We find a class of minimal hypersurfaces H-k as the zero level set of Pfaffians, resp. determinants of real 2k + 2 dimensional antisymmetric matrices. While H-1 and H-2 are congruent to the quadratic cone x(1)(2) + x(2)(2) + x(3)(2) - x(4)(2) - x(5)(2) - x(6)(2) = 0 resp. Hsiang's cubic su (4) invariant in R-15, H-k>2 (special harmonic SO (2k + 2)-invariant cones of degree >= 4) seem to be new.

  • 37.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Trzetrzelewski, Maciej
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Construction of the zero-energy state of SU(2)-matrix theory: Near the origin2009Inngår i: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 817, nr 3, s. 155-166Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We explicitly construct a (unique) Spin(9) x SU(2) singlet state, phi, involving only the fermionic degrees of freedom of the supersymmetric matrix-model corresponding to reduced 10-dimensional super-Yang Mills theory, respectively supermembranes in 11-dimensional Minkowski space. Any non-singular wave-function annihilated by the 16 supercharges of SU(2) matrix theory must, at the origin (where it is assumed to be non-vanishing) reduce to phi.

  • 38.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Trzetrzelewski, Maciej
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Octonionic twists for supermembrane matrix models2009Inngår i: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 10, nr 2, s. 339-356Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A certain G(2) x U(1) invariant Hamiltonian arising from the standard membrane matrix model via conjugating any of the supercharges by a cubic, octonionic, exponential is proven to have a spectrum covering the whole half-axis R-vertical bar. The model could be useful in determining a normalizable zero-energy state in the original SO(9) invariant SU(N) matrix model.

  • 39.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Trzetrzelewski, Maciej
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Spin(9) average of SU(N) matrix models2009Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, nr 4, s. 043510-1-043510-7Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We apply a method of group averaging to states and operators appearing in (truncations of) the Spin(9)xSU(N) invariant matrix models. We find that there is an exact correspondence between the standard supersymmetric Hamiltonian and the Spin (9) average of a relatively simple lower-dimensional model.

  • 40.
    Hoppe, Jens
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Tkachev, Vladimir G.
    Linkoping Univ, Dept Math, Linkoping, Sweden..
    New construction techniques for minimal surfaces2019Inngår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, nr 9, s. 1546-1563Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It is pointed out that despite the nonlinearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.

  • 41.
    Hoppe, Jens
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Trzetrzelewski, Maciej
    Lorentz-invariant membranes and finite matrix approximations2011Inngår i: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 849, nr 3, s. 628-635Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The question of Lorentz invariance for finite N approximations of relativistic membranes is addressed. We find that one of the classical manifestations of Lorentz invariance is no! possible for N x N matrices (at least when N = 2 or 3). How the symmetry is restored in the large N limit is studied numerically.

  • 42. Markdahl, Johan
    et al.
    Hoppe, Jens
    Wang, Lin
    Hu, Xiaoming
    A Geodesic Feedback Law to Decouple the Full and Reduced AitudeInngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956Artikkel i tidsskrift (Fagfellevurdert)
  • 43. Markdahl, Johan
    et al.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Wang, Lin
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A geodesic feedback law to decouple the full and reduced attitude2017Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 102, s. 32-41Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n - 1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.

  • 44.
    Markdahl, Johan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Wang, Lin
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Exact solutions to the closed loop kinematics of an almost globally stabilizing feedback law on SO(3)2012Inngår i: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, s. 2274-2279Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We propose a kinematic control law that solves the problem of stabilizing the attitude of a fully actuated rigid body to a desired rest attitude. The control law is designed on the special orthogonal group SO(3), thereby avoiding complications due to the representational singularities of local parametrizations and the unwinding phenomenon associated with global many-to-one parametrizations. We prove almost global stability, i.e. asymptotical stability from all initial conditions except for a set of zero measure. The proposed control law decouples the closed loop kinematics, allowing us to solve the state equations exactly for the rigid body attitude as a function of time, the initial conditions, and two gain parameters. The exact solutions provide an understanding of the transient behaviour of the system and can e.g. be used to tune the gain parameters. The geometric flavor of these ideas is illustrated by simulation.

  • 45.
    Markdahl, Johan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Thunberg, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Analytical solutions to feedback systems on the special orthogonal group SO(n)2013Inngår i: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2013, s. 5246-5251Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.

1 - 45 of 45
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