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Canonical Proper Time Formulation for Physical Systems

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Abstract

The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local time coordinates, which is the most meaningful parameterization of phenomena such as the approach to equilibrium, or the back reaction of interacting systems. We summarize the formalism of the canonical proper time framework, and provide example calculations of the eigenvalues of the hydrogen atom and near horizon description of a scalar field near a Schwarzschild black hole.

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Authors and Affiliations

  1. Computational Physics Laboratory, Howard University, Washington, DC, 20059

    James Lindesay

  2. Department of Electrical Engineering and Computational Physics Laboratory, Howard University, Washington, DC, 20059

    Tepper Gill

Authors
  1. James Lindesay
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  2. Tepper Gill
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Lindesay, J., Gill, T. Canonical Proper Time Formulation for Physical Systems. Foundations of Physics 34, 169–182 (2004). https://doi.org/10.1023/B:FOOP.0000012012.27956.d3

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  • DOI: https://doi.org/10.1023/B:FOOP.0000012012.27956.d3

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