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Title:  The stabilized PoincareHeisenberg 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 PoincareHeisenberg algebra: A Clifford algebra viewpoint. International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 16(9), pp. 15151529. 
Source:  http://dx.doi.org/10.1142/S0218271807010857 
Abstract:  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. 
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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