The stabilized PoincareHeisenberg algebra: A Clifford algebra viewpoint
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Author
Gresnigt, N.G.
Renaud, P.F.
Butler, P.H.
Date
2007Permanent Link
http://hdl.handle.net/10092/7136Abstract
The 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.
Subjects
Clifford algebraCollections
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