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On quantum field theories with finitely many degrees of freedom

Ralf Kerschner
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Abstract

The existence of inequivalent representations in quantum field theory with {\it finitely} many degrees of freedom is shown. Their properties are exemplified and analysed for concrete and simple models. In particular the relations to Bogoliubov--Valatin quasi-particles, to thermo field dynamics, and to $q$--deformed quantum theories are put foreward. The thermal properties of the non-trivial vacuum are given and it is shown that the thermodynamic equilibrium state is uniquely obtained by an irreversible vacuum dynamics. Finally, the theory is applied to a realistic model: the BCS--theory of superconductivity. An exact solution in order $O(N^{-1})$ for the full particle number conserving BCS--Hamiltonian with particle number symmetric ground state is given.

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Ralf Kerschner. 1995-05-11. On quantum field theories with finitely many degrees of freedom. https://arxiv.org/abs/hep-th/9505063

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