Computer algorithms for dirac algebra

Abstract

We present a collection of algorithms written in ALGOL 60 to illustrate the manipulation techniques used in machine language programs designed for symbolic evaluation of algebraic expressions. Such algorithms have been used by theoretical physicists in quantum electrodynamics calculations. A subset of these methods is useful in the reduction of complicated perturbation expansions which involve only ordinary (commutative) algebra. It is hoped that this will provide a more understandable and accessible archive for these methods than scattered listings of assembly code for specific computers. We consider the input and distribution of arbitrarily parenthesized algebraic expressions, Chisholm's reduction of the product of traces with intercontracted indices to single traces, the removal of contracted indices in single traces to produce simple traces which are then reduced to invariant dot products (and determinants if γ 5's are present). Several storage schemes are discussed.