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We review the formulation of fields and field equations in terms of their spinor components, based on Wigner's analysis of the Lorentz representations. This allows for a consistent physical interpretation in which fields are ascribed to an extended spin space of given dimension. Each dimension constrains the allowed symmetries and representations, and features fermions in the fundamental representation, vector bosons in the adjoint, and chirality as a good quantum number for the interactions. The gauge and flavor degrees of freedom can be related to the scalar symmetry generators in such an extended space, similarly to the Kaluza-Klein idea. At 9+1 dimensions essentially all the standard model is reproduced. This interpretation of fields leads to additional information on the Higgs mass and the coupling constants. The latter can be also obtained through a generalized argument that uses compositeness properties of the standard-model particle quantum numbers.
