Summary
The formalism of gauge fields is generalized to include changes of both phase and scale factors for external gauge groups. This enables us to construct a new Lagrangian L involving the fermion, the Yang-Mills phase gauge fields bμ ik and new scale gauge fields ei μ such that L has exact Lorentz gauge symmetry, in contrast with previous works. Gravity can be interpreted naturally as the scale gauge field of the Lorentz group. The phase gauge field leads to the prediction of a new long-range spinforce which exists between two bodies with spin densities and can be tested.
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One can apply the present formalism to other external symmetry group such as the de Sitter group which has the generators ZA = (γi/(2L),i(γjγk-γkγj)/4). See J. P. Hsu: Phys. Lett. B, 119, 328 (1982). One can consider the Poincaré group as the flat space limit (i.e., L → ∞) of the de Sitter group. According to our formalism, the generalized gauge theory with the Poincare group turns out to be the same as the theory with the Lorentz group discussed in this paper.
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Hsu, J.P. Generalized gauge fields for external-symmetry groups and gravity. Lett. Nuovo Cimento 36, 161–166 (1983). https://doi.org/10.1007/BF02887580
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DOI: https://doi.org/10.1007/BF02887580