Eliminating unphysical photon components from Dirac-Maxwell Hamiltonian quantized in the Lorenz gauge

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Futakuchi, Shinichiro¹  Usui, Kouta¹ 

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

关键词: Quantum field theory;    Dirac-Maxwell Hamiltonian;    Indefinite metric space;    Self-adjoint operators;    Gupta-Bleuler formalism;    Lorenz gauge quantization;   

DOI  :  10.1016/j.jmaa.2016.09.006

来源: Elsevier

【 摘 要 】

We study the Dirac-Maxwell model quantized in the Lorenz gauge. In this gauge, the space of quantum mechanical state vectors inevitably adopt an indefinite metric so that the canonical commutation relation (CCR) is realized in a Lorentz covariant manner. In order to obtain a physical subspace, in which no negative norm state exists, the method first proposed by Gupta and Rimier is applied with mathematical rigor. It is proved that a suitably defined physical subspace has a positive semi definite metric, and naturally induces a physical Hilbert space with a positive definite metric. Then, the original Dime-Maxwell Hamiltonian defines an induced Hamiltonian on the physical Hilbert space which is essentially self-adjoint. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free