Method for expressing Dirac spinor amplitudes in terms of invariants and application to the calculation of cross sections

We describe here a method for expressing spinor amplitudes M=ū(p′,s′)Γμ(p,s) in terms of invariants. The method also provides a simple formula for the square of M summed on spins. When Γ contains more than five terms or has more than two γ-matrices per term this formula involves the evaluation of fewer and shorter traces than the usual trace technique. Thus this should be a useful computational device for calculating cross sections. The methods presented here are independent of the spinor representation, but can be easily specialized to the important helicity case. A number of other possible applications of the amplitude formula are also briefly discussed.