Excess Structure in the Constrained Hamiltonian Formalism

Abstract Gauge theories are often characterized as possessing ‘redundancy’ or ‘excess structure’. This, in turn, motivates reducing the gauge symmetries, commonly through ‘symplectic reduction’ in the Hamiltonian framework. However, there are multiple ways to formulate a Hamiltonian gauge theory. This paper examines the relationship between the formulation of a Hamiltonian gauge theory and the attribution of excess structure. I argue that one can formulate a Hamiltonian gauge theory such that symplectic reduction does not remove structure, and there-fore that the role of symplectic reduction cannot be purely to remove ‘excess structure’. I discuss in what sense symplectic reduction is thereby motivated.