The gauge group of a toy electroweak-type model is the direct product

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Lie groups and Lie algebras: rotations, SU(2) and the double cover

Problem

The gauge group of a toy electroweak-type model is the direct product SU(2)×U(1)SU(2)\times U(1), whose elements are pairs (U,eiα)(U,e^{i\alpha}) with U∈SU(2)U\in SU(2) and eiα∈U(1)e^{i\alpha}\in U(1), combined component-wise. Find the dimension of this Lie group.

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