%0 Journal Article %1 Bohm199313 %A Bohm, Arno %A Boya, Luis J. %A Mostafazadeh, Ali %A Rudolph, Gerd %D 1993 %J Journal of Geometry and Physics %K berry topology %N 1 %P 13 - 28 %R 10.1016/0393-0440(93)90085-S %T Classification theorem for principal fibre bundles, Berry's phase, and exact cyclic evolution %U http://www.sciencedirect.com/science/article/pii/039304409390085S %V 12 %X We discuss the relation between the two mathematical interpretations of the geometric (Berry) phase, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the state vectors.

@article{Bohm199313, abstract = {We discuss the relation between the two mathematical interpretations of the geometric (Berry) phase, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the state vectors.}, added-at = {2013-02-06T00:42:27.000+0100}, author = {Bohm, Arno and Boya, Luis J. and Mostafazadeh, Ali and Rudolph, Gerd}, biburl = {https://www.bibsonomy.org/bibtex/2ea980d36fd78d74dc3448320f8e5ffa4/ttuegel}, description = {ScienceDirect.com - Journal of Geometry and Physics - Classification theorem for principal fibre bundles, Berry's phase, and exact cyclic evolution}, doi = {10.1016/0393-0440(93)90085-S}, interhash = {eda2d5a3eab4980b8d9a109623755f6f}, intrahash = {ea980d36fd78d74dc3448320f8e5ffa4}, issn = {0393-0440}, journal = {Journal of Geometry and Physics}, keywords = {berry topology}, number = 1, pages = {13 - 28}, timestamp = {2013-02-06T00:42:27.000+0100}, title = {Classification theorem for principal fibre bundles, Berry's phase, and exact cyclic evolution}, url = {http://www.sciencedirect.com/science/article/pii/039304409390085S}, volume = 12, year = 1993 }