Bargmann Invariants and Geometric Phases - a Generalised Connection

Details Bargmann Invariants and Geometric Phases - a Generalised Connection Bargmann Invariants and Geometric Phases - a Generalised Connection

1999-07-26

arxiv.org/abs/quant-ph/9907080v1

Phys.Rev.A60:3397,1999

Physics

Quantum Physics

Accepted for publication in Physical Review A

Scientific paper

10.1103/PhysRevA.60.3397

We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces. Examples of such curves are developed. Our generalisation is shown to be essential to properly understand geometric phase results in the cases of coherent states and of Gaussian states. Differential geometric aspects of null phase curves are also briefly explored.

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