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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, , associated to a principal bundle, . 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 .
@article{AMBP_2004__11_2_131_0,
author = {Aldana Dom{\'\i}nguez, Clara Luc{\'\i}a},
title = {Representation of a gauge group as motions of a {Hilbert} space},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {131--153},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {11},
number = {2},
year = {2004},
doi = {10.5802/ambp.189},
zbl = {1077.58006},
mrnumber = {2109604},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/ambp.189/}
}
TY - JOUR AU - Aldana Domínguez, Clara Lucía TI - Representation of a gauge group as motions of a Hilbert space JO - Annales mathématiques Blaise Pascal PY - 2004 SP - 131 EP - 153 VL - 11 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://geodesic.mathdoc.fr/articles/10.5802/ambp.189/ DO - 10.5802/ambp.189 LA - en ID - AMBP_2004__11_2_131_0 ER -
%0 Journal Article %A Aldana Domínguez, Clara Lucía %T Representation of a gauge group as motions of a Hilbert space %J Annales mathématiques Blaise Pascal %D 2004 %P 131-153 %V 11 %N 2 %I Annales mathématiques Blaise Pascal %U http://geodesic.mathdoc.fr/articles/10.5802/ambp.189/ %R 10.5802/ambp.189 %G en %F AMBP_2004__11_2_131_0
Aldana Domínguez, Clara Lucía. Representation of a gauge group as motions of a Hilbert space. Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 131-153. doi: 10.5802/ambp.189
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