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Dissipative scalar field theory via deformation quantization. (English) Zbl 1277.81072

Summary: The dissipative scalar field theory by means of the deformation quantization formalism is studied. Following the ideas presented by G. Dito and F. J. Turrubiates [Phys. Lett., A 352, No. 4-5, 309–316 (2006; Zbl 1187.81174)] for quantum mechanics, a star product which contains the dissipative effect for the damped oscillation modes of the field is constructed. Employing this approach the expectation values of some observables in the quantum mechanical case as well as certain correlation functions for the field case are obtained under a particular dissipative process.

MSC:

81S10 Geometry and quantization, symplectic methods
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81T99 Quantum field theory; related classical field theories

Citations:

Zbl 1187.81174
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