Real spinor fields and the electroweak interaction
type: Item
instance of: scholarly article
title: Real spinor fields and the electroweak interaction
zbMATH Open document ID: 0912.53059
published in: Journal of Functional Analysis
publication date: 1999-05-25T00:00:00Z
review text: Starting from fact that the space of real spinor fields of mass \(m>0\) on a Minkowskian spacetime is the direct sum of two irreducibly invariant subspaces under the connected Poincaré group \({\mathbf P}\), the author shows that these subspaces admit unique \({\mathbf P}\)-invariant positive-energy complex unitarizable structures in terms of which they are unitarily, and canonically, equivalent to the conventional ``left'' electron, and ``right'' positron subspaces defined by the Dirac electron. It is shown that space reversal \(P\) and time reversal \(T\) act \({\mathbf P}\)-covariantly as anti-unitary operators on these real fields and extend to complex fields in terms of which \(P\) exchanges the two subspaces while \(T\) acts separately on each subspace. When \(m=0\), the identical formalism produces a rigorous version of the usual neutrino formalism. Finally, it is shown that the real context of the usual spinor-vector interaction is equivalent to the V-A interaction, together with a computationally equivalent form of quantum electrodynamics in which the notions of a ``right'' and ``left'' electron are redundant. Contents include: an introduction; complex structures in real spinor fields; discrete symmetries; eigenstates of the basic quantum numbers; interactions in the real spinor formalism; and a discussion.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 81V10
Mathematics Subject Classification ID: 81V15
Mathematics Subject Classification ID: 81R25
zbMATH DE Number: 1216772
zbMATH Keywords: Minkowski spacetime
zbMATH Keywords: real spinor fields
zbMATH Keywords: unitarizable structures
zbMATH Keywords: space reversal
zbMATH Keywords: time reversal
zbMATH Keywords: anti-unitary operators
zbMATH Keywords: neutrino formalism
author: Irving E. Segal
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
full work available at URL: jfan.1997.3213
OpenAlex ID: W2011911691
cites work: Analysis in space-time bundles. IV: Natural bundles deforming into and composed of the same invariant factors as the spin and form bundles
cites work: COMPLEX FOURIER--BESSEL TRANSFORMS
cites work: Q4004375
cites work: Direct Formulation of Causality Requirements on the S Operator
cites work: Q5530862
cites work: Bemerkungen zur unitäräquivalenz von lorentzinvarianten feldern
cites work: Convergence of quantum electrodynamics in a curved deformation of Minkowski space
cites work: Analysis in space-time bundles. III: Higher spin bundles
DOI: 10.1006/JFAN.1997.3213
description: scientific article; zbMATH DE number 1216772