Representation of quantum field theory in an extended spin space and fermion mass hierarchy

Abstract

We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries, and their representations are determined. Symmetries are flavor or gauge-like, with fixed chirality. After spin 0, 1/2, and 1 fields are obtained in this space, we construct associated interactive gauge-invariant renormalizable terms, showing their equivalence to a Lagrangian formulation, using as example the previously studied (5+1)-dimensional case, with many standard-model connections. At 7+1 dimensions, a pair of Higgs-like scalar Lagrangian is obtained naturally producing mass hierarchy within a fermion flavor doublet.

23 pages, 5 tables. To be published in the Int. J. Mod. Phys. A

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Cited by in corpus (3)

• Heavy quarks within the electroweak multiplet
• Particles within extended-spin space: Lagrangian connection
• Heavy-quark mass relation from a standard-model boson operator representation in terms of fermions