Generalized Wentzell boundary conditions and quantum field theory

TL;DR

This paper explores free scalar fields with generalized Wentzell boundary conditions, establishing well-posedness, causality, and a holographic relation between boundary and bulk fields in quantum field theory.

Contribution

It introduces a novel class of boundary conditions for scalar fields and demonstrates their implications for causality and holography in quantum field theory.

Findings

Proves well-posedness of the classical Cauchy problem

Establishes causality for the boundary value problem

Shows a holographic relation between boundary and bulk fields

Abstract

We discuss a free scalar field subject to generalized Wentzell boundary conditions. On the classical level, we prove well-posedness of the Cauchy problem and in particular causality. Upon quantization, we obtain a field that may naturally be restricted to the boundary. We discuss the holographic relation between this boundary field and the bulk field.