Reparametrization Invariance and the Schrödinger Equation

Tkach, V. I.; Pashnev, A.; Rosales, J. J.

Reparametrization Invariance and the Schrödinger Equation

Authors

Tkach, V. I.

Pashnev, A.

Rosales, J. J.

Description

In the present work we consider a time-dependent Schrödinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schrödinger equation. The procedure is applicable in the supersymmetric theories as well. The $n=2$ supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schrödinger equation.
RevTeX,25 pages