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.Comment: 25 pages, 4 figures, v3: version accepted to JHEP. New Section V
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