Svetlichny, George Equivariance, variational principles, and the Feynman integral. (English) Zbl 1232.70044 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 032, 13 p. (2008). Summary: We argue that the variational calculus leading to Euler’s equations and Noether’s theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman’s integral. MSC: 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 49K05 Optimality conditions for free problems in one independent variable 58D30 Applications of manifolds of mappings to the sciences 70S10 Symmetries and conservation laws in mechanics of particles and systems 81S40 Path integrals in quantum mechanics Keywords:Lagrangians; calculus of variations; Euler equations; Noether theorem; equivariance; Feynman integral PDF BibTeX XML Cite \textit{G. Svetlichny}, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 032, 13 p. (2008; Zbl 1232.70044) Full Text: DOI arXiv EuDML OpenURL