On the Relation Between Quantum Mechanical and Classical Parallel Transport

Details On the Relation Between Quantum Mechanical and Classical Parallel Transport On the Relation Between Quantum Mechanical and Classical Parallel Transport

1999-08-14

arxiv.org/abs/quant-ph/9908046v1

Phys. Lett. A 266(2000)95-97

Physics

Quantum Physics

3 pages, no figures

Scientific paper

10.1016/S0375-9601(00)00013-X

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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