Dynamical similarity in higher-order classical symplectic systems

Bell, Callum and Sloan, David (2025) Dynamical similarity in higher-order classical symplectic systems. Physical Review D, 42 (4): 024014. ISSN 1550-7998

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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.