On quantum field theories with finitely many degrees of freedom

Details On quantum field theories with finitely many degrees of freedom On quantum field theories with finitely many degrees of freedom

1995-05-11

arxiv.org/abs/hep-th/9505063v1

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, LateX

Scientific paper

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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