Applications of algebraic manipulation programs in physics

Abstract

This paper describes the application to three areas of physics of computer programs that carry out formal algebraic manipulation. The application areas discussed are celestial mechanics, general relativity and quantum electrodynamics. The paper describes typical problems from each of these disciplines which can be solved using algebraic manipulative systems and presents sample programs for the solution of these problems using several algebra systems. For each discipline a review of published work acknowledging the use of algebra programs is presented and the most advanced applications are discussed in detail. In particular the Lie transform, Petrov classification and Kahane's simplification procedure are reviewed from the standpoint of algebra programs. A number of simple examples are used to introduce the reader to the capabilities of an algebra program and a brief review of the technical problems of algebraic manipulation is given. Further applications of such systems to mathematics, chemistry and engineering are briefly mentioned in the text and relevant work is referenced in the bibliography but the main emphasis is placed on applications in theoretical physics. However, the simple examples indicate, and the applications in the physical sciences confirm, that algebra systems are capable of exploitation over a much wider area than is covered in the present review. This review was completed in December 1971.