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Home > Progress of Theoretical and Experimental Physics (OUP/JPS) > Scale invariance and constants of motion |

Igata, Takahisa (Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan)

30 January 2019

**Abstract: ** Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar spacetime, only in which the symmetry is well defined and is generated by a homothetic vector. Relaxing the usual conservation condition by the Hamiltonian constraint in a particle system, we obtain a conservation law holding only on the constraint surface in the phase space. By the conservation law, we characterize constants of motion associated with the scale invariance not only for massless particles but for massive particles and classify the condition for the existence of the constants of motion. Furthermore, we find the explicit form of the constants of motion by solving the conservation equations.

**Published in: ****PTEP 2018 (2018) 063E01**
**Published by: **Oxford University Press/Physical Society of Japan

**DOI: **10.1093/ptep/pty060

**arXiv: **1804.03369

**License: **CC-BY-3.0