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  • 51.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Non-commutative geometry and exactly solvable systems2008Ingår i: INTERNATIONAL CONFERENCE ON NONCOMMUTATIVE GEOMETRY AND PHYSICS  / [ed] Wallet, J.C., 2008, Vol. 103Konferensbidrag (Refereegranskat)
    Abstract [en]

    I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system is a prototype model which provides a generalization of mean field theory taking into account non-trivial correlations which are peculiar to boson systems in two space dimensions and relevant in condensed matter physics. The prologue and epilogue contain a few remarks to relate my main story to recent developments in non-commutative quantum field theory and an addendum to our previous work together with Szabo and Zarembo on this latter subject.

  • 52.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Non-commutative Integration Calculus1995Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 36, s. 3822-3835Artikel i tidskrift (Refereegranskat)
  • 53.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Novel integrable spin-particle models from gauge theories on a cylinder1998Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 429, s. 336-342Artikel i tidskrift (Refereegranskat)
  • 54.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    On current superalgebras and super-Schwinger terms1991Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, nr 1, s. 69-76Artikel i tidskrift (Refereegranskat)
  • 55.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    On the upper critical field of anisotropic superconductors1991Ingår i: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 73, s. 347-356Artikel i tidskrift (Refereegranskat)
  • 56.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    QCD(1+1) with massless quarks and gauge covariant Sugawara construction1994Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 341, s. 195-204Artikel i tidskrift (Refereegranskat)
  • 57.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Quantum Gauge Theories and Noncommutative Geometry1996Ingår i: Acta Physica Polonica B, ISSN 0587-4254, E-ISSN 1509-5770, Vol. 27, s. 2477-2496Artikel i tidskrift (Refereegranskat)
  • 58.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model2006Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, nr 2Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter lambda, we also obtain dual relations involving mixed correlation functions of anyons with two different statistics parameters lambda and 1/lambda. We also give alternative, elementary proofs of these identities by direct computations.

  • 59.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Scattering matrix in external field problems1996Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, s. 3933-3953Artikel i tidskrift (Refereegranskat)
  • 60.
    Langmann, Edwin
    KTH, Tidigare Institutioner, Fysik.
    Second quantization of the elliptic Calogero-Sutherland model2004Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 247, nr 2, s. 321-351Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland Hamiltonian.

  • 61.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones2007Ingår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 3, s. 031-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense) set of exact eigenfunctions and corresponding eigenvalues, explicitly. Of course there is a catch to this result: if one insists on these eigenfunctions to be square integrable then the corresponding Hamiltonian is necessarily non-hermitean (and thus provides an example of an exactly solvable PT-symmetric quantum-many body system), and if one insists on the Hamiltonian to be hermitean then the eigenfunctions are singular and thus not acceptable as quantum mechanical eigenfunctions. The standard Calogero-Sutherland Hamiltonian is special due to the existence of an integral operator which allows to transform these singular eigenfunctions into regular ones.

  • 62.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Source Identity and Kernel Functions for Elliptic Calogero-Sutherland Type Systems2010Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 94, nr 1, s. 63-75Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Kernel functions related to quantum many-body systems of Calogero-Sutherland type are discussed, in particular for the elliptic case. The main result is an elliptic generalization of an identity due to Sen that is a source for many such kernel functions. Applications are given, including simple exact eigenfunctions and corresponding eigenvalues of Chalykh-Feigin-Veselov-Sergeev-type deformations of the elliptic Calogero-Sutherland model for special parameter values.

  • 63.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Strong coupling gauge theory, quantum spin systems and the spontaneous breaking of chiral symmetry1992Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 297, s. 175-180Artikel i tidskrift (Refereegranskat)
  • 64.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    SU (N) antiferromagnets and strongly coupled QED: effective field theory for Josephson junctions arrays1993Ingår i: Nuclear physics B, Proceedings supplements, ISSN 0920-5632, E-ISSN 1873-3832, Vol. 33, s. 192-208Artikel i tidskrift (Refereegranskat)
  • 65.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Supersymmetry breaking and the Jaynes-Cummings model1993Ingår i: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 176, nr 5, s. 307-312Artikel i tidskrift (Refereegranskat)
  • 66.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    The critical temperature of superconductors with a cylinder symmetrical Fermi surface1989Ingår i: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 157, nr 3, s. 415-424Artikel i tidskrift (Refereegranskat)
  • 67.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    The geometric phase and the Schwinger term in some models1992Ingår i: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 7, nr 21, s. 5045-5083Artikel i tidskrift (Refereegranskat)
  • 68.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    The Luttinger-Schwinger Model1997Ingår i: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 253, s. 310-331Artikel i tidskrift (Refereegranskat)
  • 69.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    The Superfluidity and Experimental Properties of Odd-Energy-Gap Superconductors1993Ingår i: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 26, nr 2Artikel i tidskrift (Refereegranskat)
  • 70.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Theory of the upper critical magnetic field without local approximation1989Ingår i: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 59, s. 561-569Artikel i tidskrift (Refereegranskat)
  • 71.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Towards a string representation of infrared SU(2) Yang-Mills theory1999Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 463, s. 252-256Artikel i tidskrift (Refereegranskat)
  • 72.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Laptev, Ari
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Paufler, Cornelius
    Singular factorizations, self-adjoint extensions and applications to quantum many-body physics2006Ingår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, nr 5, s. 1057-1071Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study self-adjoint operators defined by factorizing second-order differential operators in first-order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum-mechanical models such as the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.

  • 73.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Lebowitz, Joel L.
    Departments of Mathematics and Physics, Rutgers University.
    Mastropietro, Vieri
    Dipartimento di Matematica, Università degli Studi di Milano.
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Steady states and universal conductance in a quenched Luttinger model2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, s. 1-32Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.

  • 74.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik.
    Lebowitz, Joel L.
    Mastropietro, Vieri
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik.
    Time evolution of the Luttinger model with nonuniform temperature profile2017Ingår i: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, nr 23, artikel-id 235142Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the time evolution of a one-dimensional interacting fermion system described by the Luttinger model starting from a nonequilibrium state defined by a smooth temperature profile T (x). As a specific example we consider the case when T (x) is equal to T-L (T-R) far to the left (right). Using a series expansion in epsilon = 2(T-R -T-L)/(T-L + T-R), we compute the energy density, the heat current density, and the fermion two-point correlation function for all times t >= 0. For local (delta-function) interactions, the first two are computed to all orders, giving simple exact expressions involving the Schwarzian derivative of the integral of T (x). For nonlocal interactions, breaking scale invariance, we compute the nonequilibrium steady state (NESS) to all orders and the evolution to first order in epsilon. The heat current in the NESS is universal even when conformal invariance is broken by the interactions, and its dependence on T-L,T-R agrees with numerical results for the XXZ spin chain. Moreover, our analytical formulas predict peaks at short times in the transition region between different temperatures and show dispersion effects that, even if nonuniversal, are qualitatively similar to ones observed in numerical simulations for related models, such as spin chains and interacting lattice fermions.

  • 75.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner                               , Fysik.
    Lidmar, Jack
    KTH, Tidigare Institutioner                               , Fysik.
    Salmhofer, Manfred
    Wallin, Mats
    KTH, Tidigare Institutioner                               , Fysik.
    Mean field analysis of a model for superconductivity in an anti-ferromagnetic background1998Ingår i: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 296, s. 119-136Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study a lattice fermion model for superconductivity in the presence of an anti-ferromagnetic background, described as a fixed external staggered magnetic field. We discuss the possibility that our model provides an effective description of coexistence of anti-ferromagnetic correlations and superconductivity. and its possible application to high-temperature superconductivity. We also argue that, under certain conditions, this model describes a variant of the periodic Anderson model for heavy fermions. Using a path integral formulation we construct mean field equations, which we study in some detail. We evaluate the superconducting critical temperature and show thar it is strongly enhanced by anti-ferromagnetic order. We also evaluate the superconducting gap, the superconducting density of states, and the tunneling conductivity, and show that the most stable channel usually has a d(x2-y2)-wave gap.

  • 76.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Lindblad, Göran
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Fermi's Golden Rule and Exponential Decay as a RG Fixed Point2009Ingår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 134, nr 4, s. 749-768Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss the decay of unstable states into a quasicontinuum using Hamiltonian models. We show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. Using random matrices for the interaction we show that the ensemble fluctuations vanish in the scaling limit. For non-random models we can use uniformity assumptions on the density of states and the interaction matrix elements to estimate the deviations from the decay rate defined by the golden rule.

  • 77.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner                               , Fysik.
    Mickelsson, J.
    Rydh, S.
    Anomalies and Schwinger terms in NCG field theory models2001Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, nr 10, s. 4779-4801Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the quantization of chiral fermions coupled to generalized Dirac operators arising in NCG Yang-Mills theory. The cocycles describing chiral symmetry breaking are calculated. In particular, we introduce a generalized locality principle for the cocycles. Local cocycles are by definition expressions which can be written as generalized traces of operator commutators. In the case of pseudodifferential operators, these traces lead in fact to integrals of ordinary local de Rham forms. As an application of the general ideas we discuss the case of noncommutative tori. We also develop a gerbe theoretic approach to the chiral anomaly in the Hamiltonian quantization of NCG field theory.

  • 78.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Construction by bosonization of a fermion-phonon model2015Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, nr 9, artikel-id 091902Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization.We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

  • 79.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Diffusive Heat Waves in Random Conformal Field TheoryManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a non-trivial real regular contribution that depends on details of the impurities.

  • 80.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Diffusive Heat Waves in Random Conformal Field Theory2019Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, nr 2, artikel-id 020201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.

  • 81.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori. Univ Claude Bernard, Univ Lyon, ENS Lyon, CNRS,Lab Phys, F-69342 Lyon, France..
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Finite-Time Universality in Nonequilibrium CFT2018Ingår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, nr 2, s. 353-378Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

  • 82.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Sundin, Martin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Extrinsic curvature effects in brane-world scenariosArtikel i tidskrift (Övrigt vetenskapligt)
  • 83.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner                               , Fysik.
    Szabo, R. J.
    Duality in scalar field theory on noncommutative phase spaces2002Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 533, nr 02-jan, s. 168-177Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We describe a novel duality symmetry of Phi(2n)(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined with a star-product, of that which arises in quantum field theories of non-interacting scalar particles coupled to a constant background electromagnetic field. The dual models are in general of the same original form but with transformed coupling parameters, while in certain special cases all parameters are essentially unchanged. Using a particular regularization we show, to all orders of perturbation theory, that this duality also persists at the quantum level. We also point out various other properties of this class of noncommutative field theories.

  • 84.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner                               , Fysik.
    Szabo, R. J.
    Teleparallel gravity and dimensional reductions of noncommutative gauge theory2001Ingår i: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 6410, nr 10Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study dimensional reductions of noncommutative electrodynamics on flat space, which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the non-commutativity scale. The effective field theory can also contain higher curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.

  • 85.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner                               , Fysik.
    Szabo, R. J.
    Zarembo, K.
    Exact solution of noncommutative field theory in background magnetic fields2003Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 569, nr 02-jan, s. 95-101Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We obtain the exact nonperturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes nonlocally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has nontrivial interactions only when it is defined with a finite ultraviolet cutoff. We propose that small perturbations of this theory can produce solvable models with renormalizable interactions.

  • 86.
    Langmann, Edwin
    et al.
    KTH, Tidigare Institutioner, Fysik.
    Szabo, R. J.
    Zarembo, K.
    Exact solution of quantum field theory on noncommutative phase spaces2004Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, nr 1, s. 017-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an in finite-dimensional noncommutative algebra.

  • 87.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Takemura, Kouichi
    Source identity and kernel functions for Inozemtsev-type systems2012Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 53, nr 8, s. 082105-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BCN trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. We present kernel functions for Inozemtsev Hamiltonians and Chalykh-Feigin-Veselov-Sergeev-type deformations thereof. Our main result is a solution of a heat-type equation for a generalized Inozemtsev Hamiltonian which is the source of all these kernel functions. Applications are given, including a derivation of simple exact eigenfunctions and eigenvalues of the Inozemtsev Hamiltonian.

  • 88.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Triola, C.
    Balatsky, Alexander V.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA.
    Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials2019Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, nr 15, artikel-id 157001Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density n predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasilocal. In contrast, we show that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity.

  • 89.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik.
    Triola, Christopher
    Balatsky, Alexander V.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Ubiquity of superconducting domes in Bardeen-Cooper-Schrieffer theory with finite-range potentials2019Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density, n, predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasi-local. In contrast, we show that any well-defined non-local potential leads to a "superconducting dome", i.e. a non-monotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. Our results provide a prototype example and guide towards improving ab-initio predictions of Tc for real materials.

  • 90.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Wallin, Mats
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Statistisk fysik.
    Mean field magnetic phase diagrams for the two dimensional t-t '-U Hubbard model2007Ingår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 127, nr 4, s. 825-840Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the ground state phase diagram of the two dimensional t - t' - U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree-Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree-Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods.

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