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Title: Construction of dynamics and time-ordered exponential for unbounded non-symmetric Hamiltonians

We prove under certain assumptions that there exists a solution of the Schrödinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not normal. We also prove that, under the same assumptions, there exists a time evolution operator in the interaction picture and that the evolution operator enjoys a useful series expansion formula. This expansion is considered to be one of the mathematically rigorous realizations of so-called “time-ordered exponential,” which is familiar in the physics literature. We apply the general theory to prove the existence of dynamics for the mathematical model of Quantum Electrodynamics quantized in the Lorenz gauge, the interaction Hamiltonian of which is not even symmetric or normal.
Authors:
;  [1]
  1. Department of Mathematics, Hokkaido University, 060-0810 Sapporo (Japan)
Publication Date:
OSTI Identifier:
22306209
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS OF MOTION; HAMILTONIANS; HILBERT SPACE; MATHEMATICAL MODELS; QUANTUM ELECTRODYNAMICS; SCHROEDINGER EQUATION; SERIES EXPANSION