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Within the electroweak theory, it is shown that the form of the totalLagrangian is invariant, under local phase changes of the basis states forleptons and under local changes of the mathematical spaces employed for thedescription of left-handed spinor states of leptons. In doing this, acontribution from vacuum fluctuations of the leptonic fields, which causes noexperimentally-observable effect, is added to the total connection field.Accompanying the above-mentioned changes of basis states, the leptonic andconnection fields are found to undergo changes whose forms are similar to$U(1)$ and $SU(2)$ gauge transformations, respectively. These results suggest asimple physical interpretation to gauge symmetries in the electroweak theory.

Symmetries with the same forms as gauge symmetries in the electroweak theory