Fully gauge-consistent electroweak formulation of statistical symmetry

Construct a fully gauge-consistent electroweak theory incorporating the statistical U(1)×SU(2) symmetry of the stochastic scalar-doublet model.

Background

The stochastic scalar-doublet model preserves U(1)×SU(2) only at the level of probability distributions, while individual noise realizations are not invariant under local transformations. The analysis therefore distinguishes statistical symmetry from the deterministic local gauge invariance of the Standard Model.

The paper leaves unresolved whether this statistical symmetry can be embedded consistently into a complete electroweak gauge theory.

References

Whether such a statistical symmetry can be incorporated into a fully gauge-consistent electroweak theory remains an open question for future investigation.

— Statistical Symmetry Breaking and Emergent Colored Noise in a Stochastic Scalar-Doublet Field Theory  (2609.03312 - Wang, 3 Sep 2026) in Section 2, Action and symmetry