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  • 1
    Electronic Resource
    Electronic Resource
    A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6076-6095 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A derivation of the Cesàro–Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-smooth boundaries. Several results are obtained that relate the coefficients, bi, in the Shephard–Todd polynomial to the geometry of the fundamental domain. For the 3-sphere, it is shown that b4 is given by the ratio of the volume of the fundamental tetrahedron to its Schläfli reciprocal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530729
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  • 2
    Electronic Resource
    Electronic Resource
    Area-preserving diffeomorphisms of the tetrahedron (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 857-863 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Expressions for the curvature and structure constants of the area-preserving diffeomorphism group of the tetrahedron are derived. Finite-dimensional algebras are identified that yield the diffeomorphism Lie algebra in an infinite limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529343
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  • 3
    Electronic Resource
    Electronic Resource
    Erratum: Functional determinants on spheres and sectors [J. Math. Phys. 35, 4989–4999 (1994)] (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 988-988 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531171
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  • 4
    Electronic Resource
    Electronic Resource
    Central extensions of sphere groups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1433-1436 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Closed forms for the central extensions of the infinite dimensional Lie algebras of smooth maps from two- and three-spheres to compact Lie groups are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529500
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  • 5
    Electronic Resource
    Electronic Resource
    Heat kernel expansion on a generalized cone (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 770-773 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the short-time expansion of the integrated heat kernel on a locally flat generalized cone C(N), as defined by Cheeger, consists of just the Weyl volume term and the constant term. This latter is explicitly evaluated when N is a lens space, Sd/Zm (for odd d), elliptic space Sd/Z2 (for all d), and any of the three-dimensional, homogeneous space forms S3/Γ. Agreement is found with the corresponding expansion on the orbifold version, T4/Z2, of the K3 surface, and, in fact, with all TD/Z2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528395
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  • 6
    Electronic Resource
    Electronic Resource
    Quantum theory on a regular tetrahedron (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 33-38 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum theory on the surface of a regular tetrahedron is discussed. The fact that the net of the tetrahedron tiles the plane allows the propagators to be constructed as image sums of standard ones. The effect of a constant magnetic field is discussed. The field theory Casimir energy is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527806
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  • 7
    Electronic Resource
    Electronic Resource
    Functional determinants on spheres and sectors (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4989-4999 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of π). The whole sphere and hemisphere expressions are also given, in low dimensions, for both the ordinary and the conformal Laplacian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530826
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  • 8
    Electronic Resource
    Electronic Resource
    Magnetic fields and factored two-spheres (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1501-1532 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A magnetic monopole is placed at the center of a ball whose surface S2 is tiled by the symmetry group, Γ, of a regular solid. The quantum mechanics on the two-dimensional quotient S2/Γ is developed and the monopole charge is found to be quantized in an expected manner. The heat-kernel and ζ-functions are evaluated and the Casimir energy is computed. Numerical approaches to the calculation of the derivative of the Barnes ζ-function are presented. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1345501
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  • 9
    Electronic Resource
    Electronic Resource
    Smeared heat-kernel coefficients on the ball and generalized cone (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 434-452 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analyzed in detail and used to restrict the form of the heat-kernel coefficients An on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the An. As an application, the complete A5/2 coefficient is given. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1285969
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  • 10
    Electronic Resource
    Electronic Resource
    Area-preserving diffeomorphisms of Riemann surfaces (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2304-2309 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A number of Riemann surfaces are constructed by factoring the plane under the action of discontinuous groups. Expressions are found for the algebras and curvatures of the groups of area-preserving diffeomorphisms of the Riemann surfaces. The difficulties involved in finding finite algebras, which yield the diffeomorphism algebras in the infinite-dimension limit, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529153
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