Dissipation in Quantum Mechanics, Scalar and Vector Field Theory

TL;DR

This paper introduces a new minimal coupling method to model dissipation in quantum, scalar, and vector field theories, systematically analyzing energy flow and conservation in dissipative systems.

Contribution

It presents a novel formalism for dissipative quantum and field systems using coupling functions and susceptibility functions, extending previous models.

Findings

Explicit transition probability calculations for energy flow

Demonstration of energy conservation in the formalism

Generalization to scalar and vector field theories

Abstract

A new minimal coupling method is introduced. A general dissipative quantum system is investigated consistently and systematically. Some coupling functions describing the interaction between the system and the environment are introduced. Based on coupling functions, some susceptibility functions are attributed to the environment explecitly. Transition probabilities relating the way energy flows from the system to the environment are calculated and the energy conservation is explecitly examined. This new formalism is generalized to the dissipative scalar and vector field theories along the ideas developed for the quantum dissipative systems