Minimal coupling method and the dissipative scalar field theory

Abstract

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field is investigated by it's coupling to an infinite number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to the velocity is obtained for a special choice of coupling function and quantum dynamics for such a dissipative system is investigated. Some kinematical relations is calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment is obtained. © 2006 Springer Science+Business Media, Inc.