More General Momentum Dependent Gauge Transformations: Generators of Gauge Transformations Quadratic in Constraint Functions
Yusho Kagraoka · Progress of Theoretical Physics · 1993
In constrained Hamiltonian formalism a generator of infinitesimal gauge transformations is constructed as a linear combination of constraints. Usually one regards multipliers of the constraints as functions of coordinates. By evolving the multipliers to field dependent ones, a larger set of generators of gauge transformations is obtained within momentum dependent gauge transformations. This extension introduces a new class of generators of gauge transformations, whose multipliers are linear or higher order in constraint functions. Generators higher order in constraint functions are necessary for the gauge transformations to form a group. For concreteness the Yang-Mills model coupled to a fermion is analyzed. This model possesses second class constraints and thus it is also interesting in itself to investigate the generators of gauge transformations.