Exact abelian and non-abelian geometric phases

Chopin Soo, Huei Chen Lin

Research output: Contribution to journalArticlepeer-review

Abstract

The existence of Hopf fibrations S2N+1/S1 = CPN and S4K+3/S3 = HPK allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively U(1) and SU(2) fibers and complex and quaternionic projective spaces as base manifolds. This alternative method of studying quantum states and their evolution reveals the intimate connection between generic quantum mechanical systems and geometrical objects. The exact Abelian and non- Abelian geometric phases, and more generally the geometrical factors for open paths, and their precise correspondence with geometric Kähler and hyper-Kähler connections will be discussed. Explicit physical examples are used to verify and exemplify the formalism.

Original languageEnglish
Pages (from-to)85-101
Number of pages17
JournalMalaysian Journal of Mathematical Sciences
Volume8
Issue numberS
Publication statusPublished - 2014 Jan 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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