Scalar Field with Robin Boundary Conditions in the Worldline Formalism

Understand

The worldline formalism has been widely used to compute physical quantities in quantum field theory.

• However, applications of this formalism to quantum fields in the presence of boundaries have been studied only recently.
• In this article we show how to compute in the worldline approach the heat kernel expansion for a scalar field with boundary conditions of Robin type.
• In order to describe how this mechanism works, we compute the contributions due to the boundary conditions to the coefficients A_1, A_{3/2} and A_2 of the heat kernel expansion of a scalar field on the positive real line.