Dynamics of Functional Phase Space Distribution in QFT: A Third Quantization and Dynamical Unification of QFT and CMP (2212.05162v1)

Abstract: We proposed a third quantization scheme to derive the quantum dynamics of the functional phase space distribution in quantum field theory (QFT). The derivation is straightforward and algorithmic. This readily yields the ballistic quantum transport equation of QFT distribution in (p,q)- functional phase space, not in ordinary position-momentum (p,q)-space. Our starting point is the general mixed space representation in QFT. The end result serves as a unification of the quantum superfield transport theory of condensed matter physics (CMP) and QFT. This is summarized in a Table of correspondence. This third quantization scheme may have significance in quantum fluctuation theory of systems with many degrees of freedom. It may have relevance to cosmology: gravity, multi-universes, and Yang-Mills theory.