Reparametrization Invariance and the Schrödinger Equation

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

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arXiv · hep-th/9912282

Reparametrization Invariance and the Schrödinger Equation

V. I. Tkach·A. Pashnev·J. J. Rosales

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Abstract

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.

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V. I. Tkach, A. Pashnev, J. J. Rosales. 1999-12-30. Reparametrization Invariance and the Schrödinger Equation. https://arxiv.org/abs/hep-th/9912282

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