REDUCE

18.3 Additional Expression Types

Two additional expression types are necessary for high energy calculations, namely

18.3.1 Vector Expressions

These follow the normal rules of vector combination. Thus the product of a scalar or numerical expression and a vector expression is a vector, as are the sum and difference of vector expressions. If these rules are not followed, error messages are printed. Furthermore, if the system finds an undeclared variable where it expects a vector variable, it will ask the user in interactive mode whether to make that variable a vector or not. In batch mode, the declaration will be made automatically and the user informed of this by a message.

Examples:

Assuming P and Q have been declared vectors, the following are vector expressions

        p  
        2*q/3  
        2*x*y*p - p.q*q/(3*q.q)

whereas p*q and p/q are not.

18.3.2 Dirac Expressions

These denote those expressions which involve γ matrices. A γ matrix is implicitly a 4 × 4 matrix, and so the product, sum and difference of such expressions, or the product of a scalar and Dirac expression is again a Dirac expression. There are no Dirac variables in the system, so whenever a scalar variable appears in a Dirac expression without an associated γ matrix expression, an implicit unit 4 by 4 matrix is assumed. For example, g(l,p) + m denotes g(l,p) + m*unit 4 by 4 matrix. Multiplication of Dirac expressions, as for matrix expressions, is of course non-commutative.