Dirichlet to Neumann operator for abelian Yang-Mills gauge fields

TL;DR

This paper constructs a complex structure for the boundary conditions of abelian Yang-Mills fields, facilitating geometric quantization through symplectic reduction on manifolds with boundary.

Contribution

It develops a framework for the Dirichlet to Neumann operator in abelian Yang-Mills theory, enabling geometric quantization in a boundary setting.

Findings

Constructed a complex structure for boundary conditions.

Prepared a scenario for geometric quantization.

Applied symplectic reduction in a Lagrangian setting.

Abstract

We consider the Dirichlet to Neumann operator for abelian Yang- Mills boundary conditions. We treat the case for space-time manifolds with general smooth boundary components. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge. Thus we prepare a suitable scenario for geometric quantization of abelian gauge fields following a symplectic reduction procedure in a Lagrangian setting.