A symmetry of the Lagrangian in the electroweak theory
Wen-ge Wang · arXiv (Cornell University) · 2018
Within the electroweak theory, it is shown that the form of the total Lagrangian is invariant, under local phase changes of the spinor bases for leptons and under local changes of the mathematical spaces employed for the description of the left-handed spinor states of leptons. In doing this, a Lorentz-invariant term, which represents a contribution from the vacuum state and brings no experimentally-observable effect, is added to the total connection that is used in the construction of covariant derivative. Accompanying the above changes of the spinor bases and spaces, descriptions of the leptonic and connection fields are found to undergo changes, which have forms similar to $U(1)$ and $SU(2)$ gauge transformations, respectively. These results suggest a simple physical interpretation to gauge symmetries in the electroweak theory.