Group theoretic approach to fermion production

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 group SU (2) × 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) (∼ 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 dynamics. For the purpose of the demonstration, we focus on the fermion production through the derivative coupling to the pseudo-scalar.

Gravitational waves from fermion production during axion inflation

“…The fermionic coupling has not attracted as much attention, first being studied by one of us in reference [42], and, more recently, in references [43][44][45]. Due to Pauli blocking, fermions cannot undergo the same exponential amplification as the gauge fields.…”

Current survey of Clifford geometric algebra applications

“…A universal group theoretic description of the fermion production through any type of interaction with scalars or pseudo‐scalars is proposed in Min et al 183 This approach relies on the group $$$ \mathrm{SU}(2)\times \mathrm{U}(1) $$$, corresponding to the free gamma matrix choice in Clifford algebra, under which a part of the Dirac spinor function transforms like a fundamental representation. In terms of a new $$$ \mathrm{SO}(3)\left(\sim \mathrm{SU}(2)\right) $$$ vector constructed out of spinor functions, it is shown that the fermion production mechanism can be analogous to the classical dynamics of a vector precessing with angular velocity.…”