Journal of Operator Theory

Volume 64, Issue 1, Summer 2010 pp. 207-241.

Nondegeneracy of ground states in nonrelativistic quantum field theory

Authors: Tadahiro Miyao
Author institution: Institute for Fundamental Sciences, Setsunan University, 17-8 Ikeda-Nakamachi, Neyagawa, 572-8508, Japan

Summary: We reconstruct and develop the abstract Perron--Frobenius theory studied by Faris. We apply the results to some models in nonrelativistic quantum field theory and show the nondegeneracy of the gound state if it exists. The Wigner--Weisskopf model, the spin-boson model, the Fr\"ohlich polaron without ultraviolet cutoffs and the Fr\"ohlich bipolaron without ultraviolet cutoffs are discussed.

Keywords: Ground states, non-relativistic quamtum field theory, self-dual cones, Perron--Frobenius theorem.

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