# Group Theoretic Approach to Fermion Production

Research paper by Ui Min, Minho Son, Han Gyeol Suh

Indexed on: 02 Aug '18Published on: 02 Aug '18Published in: arXiv - High Energy Physics - Phenomenology

#### Abstract

We propose a universal group theoretic description of the fermion production through any type of interaction to scalar or pseudo-scalar. Our group theoretic approach relies on the residual group $SU(2) \times U(1)$, corresponding to the freedom in choosing representations of the gamma matrices in Clifford algebra, under which a part of the Dirac spinor function transforms like a fundamental representation. In terms of a new $SO(3)$ ($\sim SU(2)$) vector constructed out of spinor functions, we show that fermion production mechanism can be analogous to the classical dynamics of a vector precessing with the angular velocity. In our group theoretic approach, the equation of motion takes a universal form for any system, and choosing a different type of interaction or a different basis amounts to selecting the corresponding angular velocity. The expression of the particle number density is greatly simplified, compared to the traditional approach, and it provides us with a simple geometric interpretation of the fermion production phenomenology. For the purpose of the demonstration, we stick to the fermion production through the derivative coupling to the pseudo-scalar.