3,994 research outputs found

    Smeared heat-kernel coefficients on the ball and generalized cone

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    We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients AnA_n on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the AnA_n. As an application, the complete A5/2A_{5/2} coefficient is given.Comment: 23 pages, JyTe

    The a3/2a_{3/2} heat kernel coefficient for oblique boundary conditions

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    We present a method for the calculation of the a3/2a_{3/2} heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe

    Heat-kernel coefficients for oblique boundary conditions

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    We calculate the heat-kernel coefficients, up to a2a_2, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a breakdown of ellipticity.Comment: 9 pages, JyTeX. One reference added and minor corrections mad

    Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries

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    This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using zeta-function regularization. For a specific choice of gauge-averaging functional, the contributions to the full zeta value owed to physical degrees of freedom, decoupled gauge mode, coupled gauge modes and Faddeev-Popov ghost field are derived in detail, and alternative choices for such a functional are also studied. This analysis enables one to get a better understanding of different quantization techniques for gauge fields and gravitation in the presence of boundaries.Comment: 41 pages, plain-tex, recently appearing in Classical and Quantum Gravity, volume 11, pages 905-926, April 1994. The author wants to apologize for the delay in circulating the file, due to technical problems now fixe