Boundary dynamics and multiple reflection expansion for Robin boundary conditions

TL;DR

This paper extends the multiple reflection expansion method to Robin boundary conditions involving a boundary function S, enabling calculation of heat kernels and effective actions, with applications in quantum boundary dynamics and related physical phenomena.

Contribution

It introduces an extension of the multiple reflection expansion method to Robin boundary conditions with a boundary function S, including calculations for constant S and quadratic order with derivatives.

Findings

Derived heat kernel and effective action formulas for Robin boundary conditions.

Extended the method to include boundary functions with derivatives.

Discussed applications in symmetry breaking, tachyon condensation, and brane models.

Abstract

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)\phi =0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.