✦ LIBER ✦
Classification theorem for principal fibre bundles, Berry's phase, and exact cyclic evolution
✍ Scribed by Arno Bohm; Luis J. Boya; Ali Mostafazadeh; Gerd Rudolph
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 897 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0393-0440
No coin nor oath required. For personal study only.
✦ Synopsis
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.