Essential self-adjointness of translation-invariant quantum field models for arbitrary coupling constants

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Abstract

The Hamiltonian of a system of quantum particles minimally coupled to a quantum field is considered for arbitrary coupling constants. The Hamiltonian has a translation invariant part. By means of functional integral representations the existence of an invariant domain under the action of the heat semigroup generated by a self-adjoint extension of the translation invariant part is shown. With a non-perturbative approach it is proved that the Hamiltonian is essentially self-adjoint on a domain. A typical example is the Pauli-Fierz model with spin 1/2 in nonrelativistic quantum electrodynamics for arbitrary coupling constants.

Original languageEnglish
Pages (from-to)585-613
Number of pages29
JournalCommunications in Mathematical Physics
Volume211
Issue number3
DOIs
Publication statusPublished - Jan 1 2000
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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