Lagrangian in quantum mechanics is a connection one-form

Details Lagrangian in quantum mechanics is a connection one-form Lagrangian in quantum mechanics is a connection one-form

2003-01-24

arxiv.org/abs/quant-ph/0301133v1

Physics

Quantum Physics

7 pages, revtex 4, 1 figure

Scientific paper

We recast Dirac's Lagrangian in quantum mechanics in the language of vector bundles and show that the action is an operator-valued connection one-form. Phases associated with change of frames of reference are seen to be total differentials in the transformation of the action. The relativistic case is discussed and we show that it gives the correct phase in the non-relativistic limit for uniform acceleration.

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