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Dynamical similarity in higher-order classical symplectic systems

Callum Bell* and David Sloan†

  • *Contact author: c.bell8@lancaster.ac.uk
  • †Contact author: d.sloan@lancaster.ac.uk
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Phys. Rev. D 112, 024014 – Published 7 July, 2025

DOI: https://doi.org/10.1103/qtk7-8z92

Abstract

Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of nonstrictly conformal transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of “contact reduction” leads to theories of a frictional nature, in which the physically observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalization to theories of higher order; detailed examples are provided, and physical implications discussed.

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Phys. Rev. D 112, 024014– Published 7 July, 2025
  • Received 9 April 2025
  • Accepted 21 June 2025
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