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SL(4, R) embedding for a 3D world spinor equation

Djordje Šijački

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A generic curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the \overline{SL}(n,R) group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding \overline{SL}(3,R) vector operator Xμ, that plays the role of Dirac's γμ matrices, into \overline{SL}(4,R) . Decomposition of the unitary irreducible spinorial \overline{SL}(4,R) representations gives rise to an explicit form of the infinite Xμ matrices.


PACS

03.65.Pm Relativistic wave equations

04.62.+v Quantum fields in curved spacetime

02.10.Ud Linear algebra

MSC

81R25 Spinor and twistor methods (See also 32L25)

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81T20 Quantum field theory on curved space backgrounds

Subjects

Mathematical physics

Gravitation and cosmology

Quantum information and quantum mechanics

Dates

Issue 19 (7 October 2004)

Received 30 April 2004, in final form 30 July 2004

Published 17 September 2004



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