Abstract:
It is shown that the rules for constructing the functional integral in phase space for
systems with singular Lagrangiaus proposed by Faddeev also remain valid when gauge
conditions that depend explicitly on the time are used. Such conditions must be
considered, for example, in the case when the canonical Hamiltonian in the theory is
identically equal to zero (relativistic point particle, relativistic string, etc.). The
functional integral is first expressed in terms of the physical canonical variables,
for the separation of which a canonical transformation determined by the gauge
conditions is used. In the case of nonstationary gauge conditions, the canonical
transformation depends explicitly on the time. This leads to an additional (compared
with the case considered by Faddeev) term in the Hamiltonian that determines the
dynamics on the physical submanifold of the phase space.