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LUCY: a Clifford algebra approach to spinor calculus

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Abstract

LUCY is a MAPLE program that exploits the general theory of Clifford algebras to effect calculations involving real or complex spinor algebra and spinor calculus on manifolds in any dimension. It is compatible with both release 2 and release 3 of MAPLE V and incorporates a number of valuable facilities such as multilinearity of the Clifford product and the freedom to adopt arbitrary bases in which to perform calculations. The user can also pass with ease between the purely (real or complex) Clifford algebraic language and the more familiar matrix language. LUCY enables one to explore the structure of spinor covariant derivatives on flat or curved spaces and correlate the various spinor-inner products with the basic involutions of the underlying Clifford algebra. The canonical spinor covariant derivative is based on the Levi-Civita connection and a facility for the computation of connection coefficients has also been included. A self-contained account of the facilities available is provided together with a description of the syntax, illustrative examples for each procedure and a brief survey of the algorithms that are used in the program.