Gauge theory related studies based on constrained dynamics

Symmetry plays an important role in physics. In quantum field theory and particle physics symmetries lead to a number of very important investigations. In this context, gauge symmetry of a theory is of particular interest. Gauge Symmetry determines the form of a Lagrangian. A very interesting, elegant, and consistent way to describe a gauge theory is done with the help of constraint dynamics. Constraints in general are velocity independent relations between coordinates and momenta in the phase space of a theory. The presence of which make the ordinary Poisson bracket inadequate for its analysis and Dirac brackets come in an essential way in place of the ordinary Poisson bracket. The constraints are in general classified into two distinct classes. If Poisson brackets of a particular constraint with itself and with the other constraints of the theory are zero, then that constraint is called first class constraints else it is called the second class constraint. Quantization procedure in the presence of both the two classes of constrains are available from Dirac theory of constrained Hamiltonian system.