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Equivariance, variational principles, and the Feynman integral. (English) Zbl 1232.70044

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
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