Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-10-31
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, 1 figure, Talk given at Summer Institute 2005, Fuji-Yoshida, August 11-18, 2005 (to be published in the Proceedings)
Scientific paper
The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry becomes explicit in this formulation and specifies physical observables; the choice of a basis set which specifies the coordinates in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. It is shown that the hidden local symmetry provides a basic concept which replaces the notions of parallel transport and holonomy. We also point out that our hidden local gauge symmetry is quite different from a gauge symmetry used by Aharonov and Anandan in their definition of non-adiabatic phases.
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