  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.
