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Topological gauge theory, Cartan geo...

Wise, Derek Keith.

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Topological gauge theory, Cartan geometry, and gravity.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Topological gauge theory, Cartan geometry, and gravity./
Author:	Wise, Derek Keith.
Description:	228 p.
Notes:	Adviser: John C. Baez.
Contained By:	Dissertation Abstracts International68-06B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3270463
ISBN:	9780549090038

Topological gauge theory, Cartan geometry, and gravity.
Wise, Derek Keith.

Topological gauge theory, Cartan geometry, and gravity. - 228 p.

Adviser: John C. Baez.

Thesis (Ph.D.)--University of California, Riverside, 2007.

We investigate the geometry of general relativity, and of related topological gauge theories, using Cartan geometry. Cartan geometry---an 'infinitesimal' version of Klein's Erlanger Programm---allows us to view physical spacetime as tangentially approximated by a homogeneous 'model spacetime', such as de Sitter or anti de Sitter spacetime. This idea leads to a common geometric foundation for 3d Chern-Simons gravity, as studied by Witten, and 4d MacDowell-Mansouri gravity. We describe certain topological gauge theories, including BF theory---a natural generalization of 3d gravity to higher dimensions---as 'Cartan gauge theories' in which the gauge field is replaced by a 'Cartan connection' modeled on some Klein geometry G/H. Cartan-type BF theory has solutions that say spacetime is locally isometric to G/H itself; in this case Cartan geometry reduces to the theory of 'geometric structures'. This leads to generalizations of 3d gravity based on other 3d Klein geometries, including those in Thurston's classification of 3d Riemannian model geometries. In 4d gravity, we generalize MacDowell-Mansouri gravity to other Cartan geometries.

ISBN: 9780549090038Subjects--Topical Terms:

515831
Mathematics.

Topological gauge theory, Cartan geometry, and gravity.
LDR:03216nam 2200301 a 45 001 958329
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020 $a 9780549090038
035 $a (UMI)AAI3270463
035 $a AAI3270463
040 $a UMI $c UMI
100 1 $a Wise, Derek Keith. $3 1281787
245 1 0 $a Topological gauge theory, Cartan geometry, and gravity.
300 $a 228 p.
500 $a Adviser: John C. Baez.
500 $a Source: Dissertation Abstracts International, Volume: 68-06, Section: B, page: 3834.
502 $a Thesis (Ph.D.)--University of California, Riverside, 2007.
520 $a We investigate the geometry of general relativity, and of related topological gauge theories, using Cartan geometry. Cartan geometry---an 'infinitesimal' version of Klein's Erlanger Programm---allows us to view physical spacetime as tangentially approximated by a homogeneous 'model spacetime', such as de Sitter or anti de Sitter spacetime. This idea leads to a common geometric foundation for 3d Chern-Simons gravity, as studied by Witten, and 4d MacDowell-Mansouri gravity. We describe certain topological gauge theories, including BF theory---a natural generalization of 3d gravity to higher dimensions---as 'Cartan gauge theories' in which the gauge field is replaced by a 'Cartan connection' modeled on some Klein geometry G/H. Cartan-type BF theory has solutions that say spacetime is locally isometric to G/H itself; in this case Cartan geometry reduces to the theory of 'geometric structures'. This leads to generalizations of 3d gravity based on other 3d Klein geometries, including those in Thurston's classification of 3d Riemannian model geometries. In 4d gravity, we generalize MacDowell-Mansouri gravity to other Cartan geometries.
520 $a For BF theory in n-dimensional spacetime, we also describe codimension-2 'branes' as topological defects. These branes---particles in 3d spacetime, strings in 4d, and so on---are shown to be classified by conjugacy classes in the gauge group G of the theory. They also obey 'exotic statistics' which are neither Bose-Einstein nor Fermi-Dirac, but are governed by representations of generalizations of the braid group known as 'motion groups'. These representations come from a natural action of the motion group on the moduli space of flat G-bundles on space. We study this in particular detail in the case of strings in 4d BF theory, where Lin has called the motion group the 'loop braid group', LBn. This makes 4d BF theory with strings into a 'loop braided quantum field theory'.
520 $a We also use ideas from 'higher gauge theory' to study particles as topological defects in 4d BF theory, and find they are classified by adjoint orbits in the Lie algebra of the gauge group. Including both particles and strings in 4d BF theory leads to interesting effects, such as exotic particle/string statistics and a duality between Bohm-Aharonov effects for particles and strings.
590 $a School code: 0032.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Theory. $3 1019422
690 $a 0405
690 $a 0753
710 2 $a University of California, Riverside. $3 791122
773 0 $t Dissertation Abstracts International $g 68-06B.
790 $a 0032
790 1 0 $a Baez, John C., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3270463