Signature Change and Clifford Algebras

Details Signature Change and Clifford Algebras Signature Change and Clifford Algebras

2000-03-29

arxiv.org/abs/math-ph/0003041v1

Int.J.Theor.Phys. 40 (2001) 229-242

Physics

Mathematical Physics

11 pages, Latex file, no figures. To appear in International Journal of Theoretical Physics

Scientific paper

Given the real Clifford algebra of a quadratic space with a given signature, we define a new product in this structure such that it simulates the Clifford product of a quadratic space with another signature different from the original one. Among the possible applications of this new product, we use it in order to write the minkowskian Dirac equation over the euclidean spacetime and to define a new duality operation in terms of which one can find self-dual and anti-self-dual solutions of gauge fields over Minkowski spacetime analogous to the ones over Euclidean spacetime and without needing to complexify the original real algebra.

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