The uses of covariant formalism in analytical computation of Feynman diagrams with massive fermions

The bilinear combination of the Dirac spinors u(p1,n1)ū(p2,n2) is expressed in terms of Lorentz vectors in an explicit covariant form. The fact that the obtained expression involves but a single auxiliary vector makes that expression be very convenient for analytical computations with REDUCE (or FORM) package in the spinor formalism. Another advantage of the proposed formulas is that they apply to massive fermions, as well as to massless fermions. The proposed approach is employed for the computation of one-loop Feynman diagrams, and it is demonstrated that it considerably reduces the computation time.