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Relativistic quantum statistical mechanics in two-dimensional space-time

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Abstract

We construct for a boson field in two-dimensional space-time with polynomial or exponential interactions and without cut-offs, the positive temperature state or the Gibbs state at temperature 1/β. We prove that at positive temperatures i.e. β<∞, there is no phase transitions and the thermodynamic limit exists and is unique for all interactions. It turns out that the Schwinger functions for the Gibbs state at temperature 1/β is after interchange of space and time equal to the Schwinger functions for the vacuum or temperature zero state for the field in a periodic box of length β, and the lowest eigenvalue for the energy of the field in a periodic box is simply related to the pressure in the Gibbs state at temperature 1/β.

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Authors and Affiliations

  1. Institute of Mathematics, University of Oslo, Blindern, Oslo, Norway

    Raphael Høegh-Krohn

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  1. Raphael Høegh-Krohn
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Communicated by R. Haag and A. S. Wightman

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Høegh-Krohn, R. Relativistic quantum statistical mechanics in two-dimensional space-time. Commun.Math. Phys. 38, 195–224 (1974). https://doi.org/10.1007/BF01651542

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  • DOI: https://doi.org/10.1007/BF01651542

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