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

## TL;DR

This paper demonstrates that the electroweak Lagrangian remains invariant under certain local transformations of leptonic basis states and fields, providing a new perspective on the physical interpretation of gauge symmetries.

## Contribution

It introduces a novel interpretation of gauge symmetries in the electroweak theory as transformations of basis states and fields, including the role of vacuum fluctuations.

## Key findings

- Lagrangian invariance under local basis changes
- Leptonic and connection fields transform similarly to $U(1)$ and $SU(2)$ gauge transformations
- Vacuum fluctuations contribute to the connection field without observable effects

## Abstract

Within the electroweak theory, it is shown that the form of the total Lagrangian is invariant, under local phase changes of the basis states for leptons and under local changes of the mathematical spaces employed for the description of left-handed spinor states of leptons. In doing this, a contribution from vacuum fluctuations of the leptonic fields, which causes no experimentally-observable effect, is added to the total connection field. Accompanying the above-mentioned changes of basis states, the leptonic and connection fields are found to undergo changes whose forms are similar to $U(1)$ and $SU(2)$ gauge transformations, respectively. These results suggest a simple physical interpretation to gauge symmetries in the electroweak theory.