Abstract
In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly covariant procedure, in terms of covariant phase space with a covariant generalization of the Poisson brackets, c.q. quantum commutators. Some examples of this construction are presented.
Highlights
The discussion is framed predominantly in the language of classical dynamics, but the use of Poisson brackets and their correspondence with quantum commutators, guarantees that many results apply to the operator formulation of quantum dynamics
The main difference is the operator ordering to be implemented in quantum theory, the technicalities of which are not relevant to the issues I focus on
That G is a constant of motion if the hamiltonian is invariant under the transformations (1)
Summary
To cite this article: Jan-Willem van Holten 2015 J.
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