Unifying weak chiral symmetry for gauge and Higgs interactions (Q2774329)

The author examines new types of extended chiral transformations represented by \(2\times 2\) block matrices with coefficients of the Dirac matrices. A non-trivial toy model is considered, and the covariant derivative is partially built. A chiral algebra is built, and the building of the covariant derivative is completed using the elements of this algebra. A field strength is defined which is a natural generalization of the field strength for the gauge field. The bosonic Lagrangian is built, and the invariance of both the fermionic and the bosonic Lagrangians under the weak chiral symmetry is verified. In this way the author succeeds to develop a theory with the new chiral symmetry that effectively restricts the form of the covariant derivative for the total fermion field and the unified field strength for both gauge and Higgs fields.