A two-level Kaluza-Klein theory
The author considers a manifold P, Lie groups G and H acting on P, and pairs (\(\tau\) ',\(\tau\) '') where \(\tau\) ' is an H-invariant connection form on P fibered as a principal G-bundle over P/G and \(\tau\) '' is a G- invariant connection form on P fibered as an H-bundle over P/H. It is shown that to every pair (\(\tau\) ',\(\tau\) '') a connection form \(\mu\) in \(\rho\) (P,P/H\(\times G,H\times G)\) corresponds uniquely as well as a cross section of a vector bundle with base P/H\(\times G\). It is also shown explicitly that in the simple case \(G\times H=SU(2)\times SU(2)\) with P/H\(\times G\) identified with four-dimensional spacetime, the gauge field Lagrangian arising from the connections \(\tau\) ' and \(\tau\) '' or \(\mu\), leads to the symmetry-breaking Higgs potential.
scientific article; zbMATH DE number 4030470