Lorentz transforms of the invariant Dirac algebra
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.
scientific article; zbMATH DE number 1310374