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On the theory of non-Abelian vortices and cosmic strings


Bucher, Martin (1991) On the theory of non-Abelian vortices and cosmic strings. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5NNN-WN66.


The thesis deals with the theory of non-Abelian vortices in two spatial dimensions and cosmic strings in three spatial dimensions that arise when a non-Abelian gauge symmetry G is broken to a non-Abelian unbroken symmetry group H by the condensation of a Higgs field. The first part of the thesis discusses the case in which H is discrete. In this case all of the gauge bosons acquire a large mass; however, at low energies discretely charged particles experience non-Abelian Aharonov-Bohm scattering off vortices, which can be used to measure the flux of the vortices. Vortices also experience non-Abelian Aharonov-Bohm scattering with each other. When there are more than three vortices in a system, the Aharonov-Bohm interaction, which is described by a path integral involving sums over elements of the braid group, becomes extremely complicated. The vortices are subject to a new kind of exotic statistics. The second part of the thesis discusses the physics that arises when the requirement that H be discrete is relaxed to allow H to have one continuous generator. The vortices or strings that result change the sign of the charge for charged particles. Loops of Alice string or pairs of vortices can carry charge without any apparent source. A quantization condition for the charge carried by such pairs and loops is derived. It is also found that loops of Alice string can carry magnetic charge and that topologically stable monopoles exist in any theory with Alice symmetry breaking.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Anyons, non-Abelian statistics, quantum statistics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Group:Caltech Theory
Thesis Committee:
  • Preskill, John P. (chair)
  • Barish, Barry C.
  • Politzer, Hugh David
Defense Date:13 September 1990
Non-Caltech Author Email:bucher (AT)
Record Number:CaltechETD:etd-06132007-131249
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2577
Deposited By: Imported from ETD-db
Deposited On:06 Jul 2007
Last Modified:21 Dec 2019 02:19

Thesis Files

PDF (Bucher_m_1991.pdf) - Final Version
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