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), 325336
MSC:
Primary 81.47
MathSciNet review:
0345564
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Abstract: We present a theorem concerning the analytic domination by a semibounded selfadjoint operator H of another linear operator A which requires only the quadratic form type estimates instead of the norm estimates usually required for this type of theorem. We call the new estimates ``quadratic form type", since they are sometimes equivalent to The theorem is then applied with H the Hamiltonian for the spatially cutoff boson field model with real, bounded below, even ordered polynomial selfinteraction 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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DOI:
http://dx.doi.org/10.1090/S00029947197403455640
PII:
S 00029947(1974)03455640
Keywords:
Analytic vector,
analytic domination,
quantum fields,
bosons,
semigroup,
positivity preserving
Article copyright:
© Copyright 1974
American Mathematical Society
