Abstract
The problem of the independence of the thermodynamic limit on the boundary conditions is considered in the framework of functional integration. For every domain and every boundary condition in a sufficiently large class a functional measure is constructed and the Feynman-Kac-like formula for the statistical operator written down. Making use of some volume-independent estimates for the Green function of the heat equation, the thermodynamic limit along convex domains for general boundary conditions is proved to exist and to be equal to that for Dirichlet conditions.
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Angelescu, N., Nenciu, G. On the independence of the thermodynamic limit on the boundary conditions in quantum statistical mechanics. Commun.Math. Phys. 29, 15–30 (1973). https://doi.org/10.1007/BF01661148
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DOI: https://doi.org/10.1007/BF01661148