Reduction of Euler-Lagrange equations in gauge theories

We present a reduction procedure to the so-called canonical form for the Euler-Lagrange equations of a general gauge theory. The reduction procedure reveals constraints in the Lagrangian formulation of singular theories and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. As a demonstration we apply the reduction procedure to theories without higher derivatives.