Treatment of Landau-Ginzburg Theory with Constraints

Treatment of a singular Lagrangian with constraints using the canonical Hamiltonian approach is studied. We investigate Landau-Ginzburg theory as a constrained system using the Euler-Lagrange equation for the field system and the canonical approach. The equations of motion are obtained as total differential equations in many variables. It is shown that the simultaneous solutions of the Landau-Ginzburg theory with constraints by canonical approach lead to obtaining canonical phase space coordinates and the reduced phase space Hamiltonian without introducing Lagrange multipliers and without any additional gauge fixing condition.