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  • 1. Forger, M
    et al.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Romer, H
    Hamiltonian multivector fields and Poisson forms in multisymplectic field theory2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 11, p. 112903-Article in journal (Refereed)
    Abstract [en]

    We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.

  • 2. Grosse, Harald
    et al.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Paufler, Cornelius
    KTH, Superseded Departments, Physics.
    Exact solution of a 1D quantum many-body system with momentum-dependent interactions2004In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, no 16, p. 4579-4592Article in journal (Refereed)
    Abstract [en]

    We discuss a ID quantum many-body model of distinguishable particles with local, momentum-dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We show that the generalized model with distinguishable particles remains exactly solvable by the (coordinate) Bethe ansatz. Our solution provides a generalization of the above mentioned boson-fermion duality to particles with arbitrary exchange statistics characterized by any irreducible representation of the permutation group.

  • 3.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 22, p. 4957-4974Article in journal (Refereed)
    Abstract [en]

    As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

  • 4.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Laptev, Ari
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Paufler, Cornelius
    Singular factorizations, self-adjoint extensions and applications to quantum many-body physics2006In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, no 5, p. 1057-1071Article in journal (Refereed)
    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.

  • 5.
    Loikkanen, Juha
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Yang-Mills action from minimally coupled bosons on R-4 and on the four-dimensional Moyal plane2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 3, p. 032301-Article in journal (Refereed)
    Abstract [en]

    We consider bosons on (Euclidean) R-4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cutoff regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane R-theta(4) We also include a detailed comparison of our cutoff regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R-4 still holds if one replaces all pointwise products by the noncommutative Moyal product.

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