Hamiltonian treatment of linear field theories in the presence of boundaries: A geometric approach

Abstract

The purpose of this paper is to study in detail the constraint structure of the Hamiltonian description for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the implementation of the geometric constraint algorithm of Gotay, Nester and Hinds with special emphasis on the relevant functional analytic aspects of the problem. This is an important step toward the rigorous understanding of general field theories in the presence of boundaries, very especially when these fail to be regular. The geometric approach employed in the paper is also useful with regard to the interpretation of the physical degrees of freedom and the nature of the constraints when both gauge symmetries and boundaries are present.