Reparametrization Invariance and the Schrödinger Equation

Details Reparametrization Invariance and the Schrödinger Equation Reparametrization Invariance and the Schrödinger Equation

1999-12-30

arxiv.org/abs/hep-th/9912282v1

Physics

High Energy Physics

High Energy Physics - Theory

RevTeX,25 pages

Scientific paper

In the present work we consider a time-dependent Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger equation.

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