Quantum dissipative effects for a real scalar field coupled to a dynamical Neumann surface in d + 1 dimensions

Abstract

We study dissipative effects for a system consisting of a massless real scalar field satisfying Neumann boundary conditions on a space and time-dependent surface, in d þ 1 dimensions. We focus on the comparison of the results for this system with the ones corresponding to Dirichlet conditions, and the same surface spacetime geometry. We show that, in d ¼ 1, the effects are equal up to second order for rather arbitrary surfaces, and up to fourth order for wavelike surfaces. For d > 1, we find general expressions for their difference.