Study of gauge symmetry in the velocity phase space through Lagrangian formulation: some case studies

Gauge symmetry of some models is investigated through Lagrangian formulation in the velocity phase space. It is found that the Lagrangian formulation is a useful instrument to verify whether a given model has gauge symmetry or not. It can derive the complete set of gauge transformation generators of a Lagrangian. The prescription based on Lagrangian formulation has ability to show a direction towards the extension of phase space introducing auxiliary fields to restore the gauge symmetry. It has been found that this prescription works well in the usual phase space as well as extended phase space. (author)