Polar decomposition of a Dirac spinor

Details Polar decomposition of a Dirac spinor Polar decomposition of a Dirac spinor

2002-07-30

arxiv.org/abs/hep-th/0207262v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX

Scientific paper

Local decompositions of a Dirac spinor into `charged' and `real' pieces psi(x) = M(x) chi(x) are considered. chi(x) is a Majorana spinor, and M(x) a suitable Dirac-algebra valued field. Specific examples of the decomposition in 2+1 dimensions are developed, along with kinematical implications, and constraints on the component fields within M(x) sufficient to encompass the correct degree of freedom count. Overall local reparametrisation and electromagnetic phase invariances are identified, and a dynamical framework of nonabelian gauge theories of noncompact groups is proposed. Connections with supersymmetric composite models are noted (including, for 2+1 dimensions, infrared effective theories of spin-charge separation in models of high-Tc superconductivity).

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