Abstract
In terms of a 4-component spinor-isospinor Weyl-type constituent field, a unique Lagrangian ~det[χ(n)χ*(n)] can be constructed on a space-time lattice with the large symmetry groupU1⊗SL4,C,loc—or essentially a subgroupU1⊗SU4,loc by taking the quantization condition into account—as invariance group. The invariance under local transformations in this framework is established without introducing additional vector gauge fields. In the continuum limit the Lagrangian obtains the form of a non-Abelian gauge-invariant spinor Lagrangian where effective vector gauge fields and certain effective Higgstype fields occur on the same level as, respectively, vectorial and scalar (or tensorial) bilinear local composites of the constituent spinor field. Physical spinor fields appear as trilinear local composites. The effective Lagrangian—with appropriate interpretation given elsewhere—reflects the salient features of the Glashow-Weinberg-Salam model, but contains additional Abelian and non-Abelian gauge-type interactions.
Published Version
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