Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 032, 13 pages      arXiv:0711.4550      http://dx.doi.org/10.3842/SIGMA.2008.032
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Equivariance, Variational Principles, and the Feynman Integral

George Svetlichny
Departamento de Matemática, Pontifícia Unversidade Católica, Rio de Janeiro, Brazil

Received November 02, 2007, in final form March 13, 2008; Published online March 19, 2008

Abstract
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.

Key words: Lagrangians; calculus of variations; Euler's equations; Noether's theorem; equivariance; Feynman's integral.

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