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Finite temperature quantum field theory in the heat kernel method

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Abstract

The heat kernel trace in a (D+1)-dimensional Euclidean spacetime is used to derive free energy in the finite temperature field theory. The spacetime presents a D-dimensional compact space (domain) with a (D-1)-dimensional boundary, and one closed dimension, whose volume is proportional to Planck’s inverse temperature. The thermal sum arises due to the topology of the closed Euclidean time. The free energy thus obtained is a functional of the Planck’s inverse temperature and the geometry of the system. Its ‘high temperature’ asymptotic expressions, given for (3+1) and (2+1) dimensions, contain two contributions defined by the volume of the domain and by the volume of boundary of the domain. No universal asymptotic of free energy exists while approaching the absolute zero temperature, which is forbidden topologically.

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Authors and Affiliations

  1. Lebedev Research Center in Physics, Leninskii Prospekt 53, Moscow, 119991, Russia

    Yu. V. Gusev

  2. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476, Golm, Germany

    Yu. V. Gusev

  3. Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres, 91440, Bures-sur-Yvette, France

    Yu. V. Gusev

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Gusev, Y.V. Finite temperature quantum field theory in the heat kernel method. Russ. J. Math. Phys. 22, 9–19 (2015). https://doi.org/10.1134/S1061920815010033

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