Derivation of Transport Equations using the Time-Dependent Projection Operator Method

TL;DR

This paper introduces a formalism using a time-dependent projection operator in quantum field theory to derive coupled transport equations and Langevin-type equations without convolution terms, enabling systematic coarse-graining.

Contribution

It presents a novel formalism for coarse-graining in quantum field theory using a time-dependent projection operator and derives new coupled transport equations.

Findings

Derived Langevin-type equations without convolution integrals

Developed a systematic perturbative expansion method

Applied the formalism to a quantum field theoretical model

Abstract

We develop a formalism to carry out coarse-grainings in quantum field theoretical systems by using a time-dependent projection operator in the Heisenberg picture. A systematic perturbative expansion with respect to the interaction part of the Hamiltonian is given, and a Langevin-type equation without a time-convolution integral term is obtained. This method is applied to a quantum field theoretical model, and coupled transport equations are derived.