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On the Relation Between Quantum Mechanical and Classical Parallel Transport

Quantum Physics 2009-10-31 v1 Mathematical Physics Differential Geometry math.MP

Abstract

We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators whose commutators yield diagonal operators; or in Lie algebras those operators whose commutators are in the (diagonal) Cartan subalgebra.

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Cite

@article{arxiv.quant-ph/9908046,
  title  = {On the Relation Between Quantum Mechanical and Classical Parallel Transport},
  author = {J. Anandan and L. Stodolsky},
  journal= {arXiv preprint arXiv:quant-ph/9908046},
  year   = {2009}
}

Comments

3 pages, no figures