Fiber bundles in quantum physics

The theory of fiber bundles provides a natural setting for the description of macroscopic quantum systems, wherein their classical and quantum features are represented by actions on the base manifolds and the fibers, respectively, of the relevant bundles. We provide realizations of this picture in the description of (a) quasiparticle excitations of many-body systems, especially those in superfluid helium, (b) the interplay between the microscopic and macroscopic dynamics in certain irreversible processes, such as that of a laser, and (c) local thermodynamic equilibrium. In particular, (b) involves the treatment of a dynamical system which is defined on a vector bundle.

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