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 $SU(2)\times U(1)$, 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 dynamics. For the purpose of the demonstration, we focus on the fermion production through the derivative coupling to the pseudo-scalar.

arXiv comment25 pages, 4 figures, v3: version accepted to JHEP. New Section V added

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Cited by in corpus (5)

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• The Different Regimes of Axion Gauge Field Inflation
• Cosmological Relaxation from Dark Fermion Production
• Fermionic Particle Creation in Curved Spacetime: Physical Bloch-Vector Dynamics and Exact de Sitter Scaling