Treatment of Landau-Ginzburg Theory with Constraints

TL;DR

This paper explores how to handle Landau-Ginzburg theory as a constrained system using the canonical Hamiltonian method, deriving equations of motion and phase space without Lagrange multipliers or gauge fixing.

Contribution

It demonstrates a canonical approach to Landau-Ginzburg theory that avoids Lagrange multipliers and gauge fixing, simplifying the constrained system analysis.

Findings

Derived equations of motion as total differential equations in multiple variables.

Obtained canonical phase space coordinates and reduced Hamiltonian without Lagrange multipliers.

Showed the method's effectiveness in handling constraints in Landau-Ginzburg theory.

Abstract

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.