Reformulation and Extension of the Standard Model

We present a classically equivalent reformulation of the Standard Model. In this framework, the Higgs doublet is recast as a $2\times 2$ matrix and right-handed fermion singlets are organized into novel doublets. This restructuring reveals a latent algebraic geometry that naturally realizes a new local gauge principle: the $\mathbf{\text{extended}}\mathbf{\text{Weyl}}\mathbf{\text{symmetry}}$. Generalizing Hermann Weyl’s 1929 idea of local scale invariance to internal multiplet spaces, this symmetry extends the scope of local gauge symmetries beyond the conventional Yang–Mills framework and provides the foundation for a classical extension of the Standard Model. The resulting theory introduces new gauge bosons (potential dark matter candidates) and a second scalar field. Weyl symmetry breaking renders this additional scalar non-dynamical and leaves the observed Higgs boson as the sole dynamical scalar. The extended Weyl symmetry also leads to several notable theoretical consequences: (i) parity violation is embedded within an underlying parity-symmetric structure; (ii) the minus sign of the Higgs potential is uniquely fixed by the symmetry breaking pattern rather than chosen $\mathit{\text{by}}\mathit{\text{hand}}$; and (iii) a right-handed neutrino is required by the doublet structure, with its masslessness protected by the extended Weyl symmetry. Quantum aspects of this framework – particularly potential gauge anomalies and renormalizability – remain open and warrant dedicated investigation.