Annales Mathématiques
Blaise Pascal
no. 2
Representation of a gauge group as motions of a Hilbert space
Clara Lucía Aldana Domínguez1
1 Universidad de los Andes Department of Mathematics Cr 1 No. 18 A 10 Bogotá D.C Colombia
Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 131-153.

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.

DOI : 10.5802/ambp.189
Clara Lucía Aldana Domínguez 1

1 Universidad de los Andes Department of Mathematics Cr 1 No. 18 A 10 Bogotá D.C Colombia 
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Clara Lucía Aldana Domínguez. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.189/

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