2026-09-22T09:21:55Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/20709 2023-07-10 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Stone, Michael Goff, William Eugene 2011-05-07T12:47:03Z 2011-05-07T12:47:03Z 10000-01-01 1989 When quantized fermions are coupled to a background field, nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superfluid $\sp3$He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the $\sp3$He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero ground-state Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work. Made available in DSpace on 2011-05-07T12:47:03Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010865.pdf: 4808812 bytes, checksum: 2da4882e19f9dcc2de4e7ec8c5ba5300 (MD5) Previous issue date: 1989 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:45:44Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:20:19-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9010865 (UMI)AAI9010865 http://hdl.handle.net/2142/20709 eng Copyright 1989 Goff, William Eugene Physics, General Physics, Condensed Matter Physics, Elementary Particles and High Energy Two applications of Berry's phase in fermionic field theory text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.