Geometry of gauge fields in a multidimensional universe

✍ Scribed by A. Jadczyk; K. Pilch

• Publisher: Springer
• Year: 1984
• Tongue: English
• Weight: 338 KB
• Volume: 8
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00406391

✦ Synopsis

Let S be a group of automorphisms of a principal fibre bundle (U, 7r, E, R), both groups S and R being compact. Let I (resp. H) be the isotropy group o f S (resp. S x R) acting on E (resp. U), and let N(/) (resp. N(H)) be the normalizer o f I (resp.H) inS (resp. S x R). We construct two principal bundles P(M, N(I) I I) C E and Q(M, N(H) I H) C U, where M = E/S is the space of orbits of S in E, and we prove that, given a connection A in P, there is a one-to-one correspondence between S-invariant connections w in U and triples (B, qs, if), where B is a connection in Q, part of which is a pullback 7r*A of A, and qs, ~ are scalars which are crosssections of certain vector bundles associated with Q. The resulting final gauge group N(H) I H is shown to contain as a normal subgroup the 'centralizer o f / i n R', known from earlier works of other authors. A dimensional reduction of the Einstein-Yang-Mills system on E is briefly discussed.