Boundary conditions as constraints

TL;DR

This paper introduces a novel method for computing the symplectic structure of quantum field theories with boundary conditions by treating them as second class constraints, enhancing the understanding of boundary effects in holographic contexts.

Contribution

It proposes a new approach to handle boundary conditions as constraints, and explores the inverse holographic map to relate boundary theories to boundary-less constrained theories.

Findings

Boundary conditions can be effectively treated as second class constraints.

The inverse holographic map provides a useful perspective for boundary theories.

The method improves the computation of symplectic structures in constrained quantum field theories.

Abstract

A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class constraints in the sense of the Dirac's method. However, we show that this proposal is more useful if we consider an inverse of the Holographic map between a theory defined in the boundary to another with constraints but without boundary.