Hamiltonian of Mean Force and Dissipative Scalar Field Theory

Abstract

In the framework of the Hamiltonian of mean force, internal energy, free energy and entropy of a dissipative scalar field are obtained.Dissipative scalar field theories appear in important problems in classical and quantum physics. For example in Casimir Physics there are some special geometries where electromagnetic field can be basically considered as two independent scalar fields. Then these scalar fields should be quantized in the presence of a nonhomogeneous magnetodielectric medium where absorption and dispersion properties are taken into account [1,2,3,4]. For the classical case one can model the fluctuating media by a collection of scalar fields and study the fluctuation-induced forces among immersed objects in such a medium [?].The main obstacle in quantizing a dissipative field is that a Lagrangian or a Hamiltonian is required that generate the quantum evolution of the system and this leads to difficulties in implementing the canonical commutation relations if we are not allowed to include a heath bath [5,6]. Various approaches to quantize a dissipative system have been introduced. Among these approaches, the system plus reservoir scheme allows the quantization of the total system described by a time-independent Hamiltonian in a rigorous way.