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.
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