The geometry of the classical action in phase space
Year: 2025
Type: article
Abstract: We present a geometric representation in phase space of the classical action. Specifically, we find three seemingly unrelated interpretations for the action as the sum of signed areas of shapes in phase space. By using the Poincaré-Cartan integral invariants in extended phase space, we are able to show the equivalence between all three. As a concrete example, we consider the 1D harmonic oscillator, but the results are general for arbitrary potentials and numbers of dimensions.
Source: The Journal of Chemical Physics
DOI: 10.1063/5.0300889
Authors: Itay Blank, David J. Tannor
Institution: Weizmann Institute of Science
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,500
Awards: G2916447197, G5770503703
OpenAlex ID: W4417116473