40 research outputs found
Equivariance, Variational Principles, and the Feynman Integral
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.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA