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.

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Correspondence to Minho Son.

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ArXiv ePrint: 1808.00939

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Min, U., Son, M. & Suh, H.G. Group theoretic approach to fermion production. J. High Energ. Phys. 2019, 72 (2019). https://doi.org/10.1007/JHEP03(2019)072

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Keywords

  • Cosmology of Theories beyond the SM
  • Beyond Standard Model