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Title: The stabilized Poincare-Heisenberg algebra: A Clifford algebra viewpoint
Authors: Gresnigt, N.G.
Renaud, P.F.
Butler, P.H.
Keywords: Clifford algebra
Poincare algebra
algebraic stability
Issue Date: 2007
Citation: Gresnigt, N.G., Renaud, P.F., Butler, P.H. (2007) The stabilized Poincare-Heisenberg algebra: A Clifford algebra viewpoint. International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 16(9), pp. 1515-1529.
Source: http://dx.doi.org/10.1142/S0218271807010857
Abstract: 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.
Publisher: University of Canterbury. Mathematics and Statistics
University of Canterbury. Physics and Astronomy
Research Fields: Field of Research::01 - Mathematical Sciences::0105 - Mathematical Physics
Field of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010101 - Algebra and Number Theory
URI: http://hdl.handle.net/10092/7136
Rights URI: http://library.canterbury.ac.nz/ir/rights.shtml
Appears in Collections:Engineering: Journal Articles

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