Analytic domination with quadratic form type estimates and nondegeneracy of ground states in quantum field theory

Author:
Alan D. Sloan

Journal:
Trans. Amer. Math. Soc. **194** (1974), 325-336

MSC:
Primary 81.47

DOI:
https://doi.org/10.1090/S0002-9947-1974-0345564-0

MathSciNet review:
0345564

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Abstract: We present a theorem concerning the analytic domination by a semi-bounded selfadjoint operator *H* of another linear operator *A* which requires only the quadratic form type estimates

*H*the Hamiltonian for the spatially cutoff boson field model with real, bounded below, even ordered polynomial self-interaction in one space dimension and , the conjugate momentum to the free field. When the underlying Hilbert space of this model is represented as where

*dq*is a probability measure on

*Q*, the spectrum of the von Neumann algebra generated by bounded functions of certain field operators, then

*maximizes support*in the sense that is nonzero almost everywhere whenever

*f*is not identically zero.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0345564-0

Keywords:
Analytic vector,
analytic domination,
quantum fields,
bosons,
semigroup,
positivity preserving

Article copyright:
© Copyright 1974
American Mathematical Society