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Essential Self-Adjointness of¶Translation-Invariant Quantum Field Models¶for Arbitrary Coupling Constants

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.

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Received: 26 May 1999 / Accepted: 9 November 1999

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Hiroshima, F. Essential Self-Adjointness of¶Translation-Invariant Quantum Field Models¶for Arbitrary Coupling Constants. Comm Math Phys 211, 585–613 (2000). https://doi.org/10.1007/s002200050827

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  • DOI: https://doi.org/10.1007/s002200050827

Keywords

  • Integral Representation
  • Field Model
  • Quantum Electrodynamic
  • Quantum Particle
  • Invariant Part