Flavour-coherent propagators and Feynman rules: Covariant cQPA formulation

TL;DR

This paper simplifies and generalizes the derivation of flavour-coherent propagators and Feynman rules in fermionic kinetic theory, revealing their composite structure and extending applicability to nonzero self-energy cases.

Contribution

It introduces a covariant formulation of cQPA that explicitly shows the spectral and interaction structure, extending previous work to include nonzero dispersive self-energy effects.

Findings

Revealed the composite nature of cQPA Wightman functions.

Derived flavoured kinetic equations similar to density matrix equations.

Extended the formalism to cases with nonzero dispersive self-energy.

Abstract

We present a simplified and generalized derivation of the flavour-coherent propagators and Feynman rules for the fermionic kinetic theory based on coherent quasiparticle approximation (cQPA). The new formulation immediately reveals the composite nature of the cQPA Wightman function as a product of two spectral functions and an effective two-point interaction vertex, which contains all quantum statistical and coherence information. We extend our previous work to the case of nonzero dispersive self-energy, which leads to a broader range of applications. By this scheme, we derive flavoured kinetic equations for local 2-point functions $S^{<,>}_\mathbf{k}(t,t)$, which are reminiscent of the equations of motion for the density matrix. We emphasize that in our approach all the interaction terms are derived from first principles of nonequilibrium quantum field theory.