Covariant gauges for constrained systems

The conventional Dirac gauge-fixing approach for degenerate theories is generalized with the aim to include covariant gauge conditions in the consideration. For this purpose a method to construct an extended phase space without Grassmann variables is proposed. For a given gauge depending on the velocities and accelerations up to order k, the extension of the phase space is carried out by rewriting the original theory in the form of a theory with higher-order derivatives (the highest order is k + 1) and applying to the latter the Ostrogradsky method of Hamiltonian description. As a result, the covariant gauge in extended phase space can be employed in the same manner as the unitary one.