The stabilized PoincareHeisenberg algebra: A Clifford algebra viewpoint
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2007Permanent Link
http://hdl.handle.net/10092/7136The stabilized PoincareHeisenberg 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 semisimple 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 spacetime and instead to work in spacetimemomentum.
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Clifford algebraCollections
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