Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez[1]

  • [1] Universidad de los Andes Department of Mathematics Cr 1 No. 18 A 10 Bogotá D.C Colombia

Annales mathématiques Blaise Pascal (2004)

  • Volume: 11, Issue: 2, page 131-153
  • ISSN: 1259-1734

Abstract

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This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second part is about the definition of the gauge group, 𝔊 P , associated to a principal bundle, P . In the third part we present the construction of the Hilbert space where the representation takes place. Finally, in the fourth part, we show the construction of the representation and the way in which this representation goes to the set of connections associated to P .

How to cite

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Aldana Domínguez, Clara Lucía. "Representation of a gauge group as motions of a Hilbert space." Annales mathématiques Blaise Pascal 11.2 (2004): 131-153. <http://eudml.org/doc/10502>.

@article{AldanaDomínguez2004,
abstract = {This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second part is about the definition of the gauge group, $\{\mathfrak\{G\}\}_\{P\}$, associated to a principal bundle, $P$. In the third part we present the construction of the Hilbert space where the representation takes place. Finally, in the fourth part, we show the construction of the representation and the way in which this representation goes to the set of connections associated to $P$.},
affiliation = {Universidad de los Andes Department of Mathematics Cr 1 No. 18 A 10 Bogotá D.C Colombia},
author = {Aldana Domínguez, Clara Lucía},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {7},
number = {2},
pages = {131-153},
publisher = {Annales mathématiques Blaise Pascal},
title = {Representation of a gauge group as motions of a Hilbert space},
url = {http://eudml.org/doc/10502},
volume = {11},
year = {2004},
}

TY - JOUR
AU - Aldana Domínguez, Clara Lucía
TI - Representation of a gauge group as motions of a Hilbert space
JO - Annales mathématiques Blaise Pascal
DA - 2004/7//
PB - Annales mathématiques Blaise Pascal
VL - 11
IS - 2
SP - 131
EP - 153
AB - This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second part is about the definition of the gauge group, ${\mathfrak{G}}_{P}$, associated to a principal bundle, $P$. In the third part we present the construction of the Hilbert space where the representation takes place. Finally, in the fourth part, we show the construction of the representation and the way in which this representation goes to the set of connections associated to $P$.
LA - eng
UR - http://eudml.org/doc/10502
ER -

References

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