Lorentz transforms of the invariant Dirac algebra
type: Item
instance of: scholarly article
title: Lorentz transforms of the invariant Dirac algebra
zbMATH Open document ID: 0936.35204
DOI: 10.1007/BF01332489
published in: Integral Equations and Operator Theory
publication date: 2000-02-03T00:00:00Z
review text: The author discusses the invariance under space-time transformations of the Dirac algebra -- the invariant algebra of pseudodifferential operators of the Dirac propagator introduced and discussed in the author's papers [\textit{H. O. Cordes}, Manuscr. Math. 45,77-105 (1983; Zbl 0562.35079); Commun. Partial Differ. Equ. 8, 1475-1485 (1983; Zbl 0539.35057); The technique of pseudodifferential operators, London Math. Soc. Lecture Notes 202, Cambrige Univ. Press (1995; Zbl 0828.35145)]. In more details, let \(H\) be the Dirac Hamiltonian, and \(e^{-iHt}\) be a unitary operator of \(\mathbb{H}=L_2(\mathbb{R}^3,\mathbb{C}^4)\). The pseudodifferential operator \(A\) belongs to the invariant algebra if \(e^{iHt}Ae^{-iHt}\) is again a pseudodifferential operator for all \(t\). The author considers the relation between two invariant algebras at \(t=0\) and at \(t'=0\) when \((t,x)\) and \((t',x')\) are Minkowski space coordinates related by a proper Lorentz transform.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47L90
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 83A05
zbMATH DE Number: 1310374
zbMATH Keywords: space-time transformations
zbMATH Keywords: Dirac algebra
zbMATH Keywords: Dirac propagator
zbMATH Keywords: Dirac Hamiltonian
zbMATH Keywords: Lorentz transform
author: Heinz Cordes
reviewed by: Vladimir Rabinovich
MaRDI profile type: Publication
cites work: A pseudo-algebra of observables for the Dirac equation
cites work: A version of Egorov's theorem for systems of hyperbolic pseudo- differential equations
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cites work: Q4328330
cites work: Quantum field theory techniques in graphical enumeration
full work available at URL: https://doi.org/10.1007/bf01332489
OpenAlex ID: W2024386689
description: scientific article; zbMATH DE number 1310374