Nonsingular constraints in time-dependent variational principle for parametrized wave functions

摘要

In this work, we consider two conditions required for the nonsingularity of constraints in the time-dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second-class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP-parameters, the regularity and the second-class conditions become equivalent. The second-class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second-class condition in an extended canonical phase-space.