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 $M=\overline{u}(p^{\prime },s^{\prime })\Gamma \mu \mathrm{}(p,s)\mathrm{}$ in terms of invariants. The method also provides a simple formula for the square of $M$ summed on spins. When $\Gamma$ contains more than five terms or has more than two $\gamma$-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.