The Trace Formula of the Spinoriel Amplitude

TL;DR

This paper introduces a novel trace formula for fermion probability amplitudes expressed over spinor indices, simplifying calculations and enabling new computational approaches in quantum field theory.

Contribution

It presents the first formulation of fermion amplitudes as a trace over spinor indices, unifying amplitude and probability calculations at the computational level.

Findings

Automated calculation of fermion charge-current using symbolic programs

Simplified analytic computation of quark dipole magnetic moments

Enhanced transparency of Fierz rearrangement identities

Abstract

We re express the fermion's probability amplitude as a trace over spinor indices, which formulation surprisingly does not exist in literature. This formulation puts the probabilty amplitude and the the probabilty(squared amplitude) of a given process on equal footing at the compuational level and this is our principal motivation to write the present paper. We test the power of the trace formula in three applications: Calculation of the charge-current of fermions by using symbolic programs, which current so far was only computable by hand, analytic compuation of the quark dipole magnetic moment, rendered less cumbersome, and finally Fiertz rearrangement identities now made more transparent.