Berry’s geometric phase is a correction to the wave function arising in the study of adiabatic quantum systems; it has been discovered by M. V. Berry. There are analogous effects for other wave phenomena; there has been also much earlier work of Pancharatnam on the related phenomenon in optics. The origin of the Berry’s phase is in nonflatness of a parallel transport which appears in the corresponding phase factors.
Michael Berry, Quantal phase factors accompanying adiabatic changes, Proc. Roy. Soc. London Ser. A 392 (1984), no. 1802, 45–57, doi
Michael Berry, The quantum phase, five years after, in: Geometric phases in physics, 7–28, Adv. Ser. Math. Phys., 5, World Sci. Publ., Teaneck, NJ, 1989.
Barry Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Phys. Rev. Lett. 51 (1983), no. 24, 2167–2170, MR85e:81024
J. M. Robbins, Michael Berry, The geometric phase for chaotic systems, Proc. Roy. Soc. London Ser. A 436 (1992), no. 1898, 631–661, doi, 94a:81036
V. I. Arnold, Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect,
Selecta Mathematica 1:1, 1–19 (1995) doi
Dariusz Chruściński, Andrzej Jamioƚkowski, Geometric phases in classical and quantum mechanics, Progress in Math. Physics 36, Birkhäuser 2004. xiv+333 pp. ISBN: 0-8176-4282-X
Mikio Nakahara, Chapter 10.6 of: Geometry, Topology and Physics, IOP 2003 (doi:10.1201/9781315275826, pdf)
A relation to Chern-Bott connection is explained in 4.1 of lecture notes
Mauro Spera, Geometric methods of quantum mechanics, J. Geometry and Symmetry in Physics 24 1-44 (2011) euclid
D. Rohrlich, Berry’s phase, entry in Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear; arxiv/0708.3749
wikipedia: geometric phase
<http://www.mi.infm.it/manini/berryphase.html>
Frank Wilczek, Alfred Shapere, Geometric phases in physics, World Scientific, 1989
M. O. Katanaev, On geometric interpretation of the Berry phase, Rus. Phys. J. 54(2012)1082–1092, Izv. VUZov. Fizika 10(2011) 26–35 arxiv/1212.1782
Maxim Braverman, The Berry phase and the phase of the determinant, arxiv/1310.6332
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