Geometric phase and chiral anomaly; their basic differences

Abstract

All the geometric phases are shown to be topologically trivial by using the second quantized formulation. The exact hidden local symmetry in the Schrödinger equation, which was hitherto unrecognized, controls the holonomy associated with both of the adiabatic and non-adiabatic geometric phases. The second quantized formulation is located in between the first quantized formulation and the field theory, and thus it is convenient to compare the geometric phase with the chiral anomaly in field theory. It is shown that these two notions are completely different.

15 pages

References in corpus (9)

• Geometric phases for mixed states in interferometry
• Geometric phases for non-degenerate and degenerate mixed states
• Second quantized formulation of geometric phases
• Geometric phases and hidden local gauge symmetry
• Topological properties of Berry's phase
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• Geometric phases for mixed states and decoherence
• Adiabatic approximation in the second quantized formulation
• Geometric phases, gauge symmetries and ray representation