Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-02
Int.J.Mod.Phys.D16:1519-1529,2007
Physics
High Energy Physics
High Energy Physics - Theory
14 pages
Scientific paper
10.1142/S0218271807010857
The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after attempting to combine the Lie algebras of quantum mechanics and relativity which by themselves are stable, however not when combined. In this paper we show how the sixteen dimensional Clifford algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional stability considerations, relying instead on the fact that CL(1,3) is a semi-simple algebra and therefore stable. It is therefore conceptually easier and more straightforward to work with a Clifford algebra. The Clifford algebra path suggests the next evolutionary step toward a theory of physics at the interface of GR and QM might be to depart from working in space-time and instead to work in space-time-momentum.
Butler Philip H.
Gresnigt Niels G.
Renaud Peter F.
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