Submissions from R. A. Nascimento
- [1] faKiv:2404.07806 [pdf]
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Compactification in higher-spin fields with massless synchronous couplingsComments: 12 pages, 2 figures
We study compactification effects in the $SU(3)$ Chern-Simons theory of higher-spin fields with massless synchronous couplings, by performing the standard 1/2-Chern-Simons decomposition in terms of the 1/4-Chern-Simons decomposition. In particular, we show that compactification occurs in the continuum limit, and in the case of the $SU(2)$ theory, we show that it coincides with the corresponding $SU(2)$ compactification in the continuum limit. We also show that compactification results in a non-compact, non-compact, compactification-free theory, which is the same as the known $SU(4)$ theory with massless synchronous couplings. Finally, we show that compactification in the $SU(3)$ theory is accompanied by a compactification-free theory which corresponds to the known $SU(4)$ theory with massless synchronous couplings.
- [2] faKiv:2404.08264 [pdf]
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The geometrical nature of the $2+1$-dimensional Higgs modelComments: 12 pages, 1 figure
It has been known that the Higgs model in the $2+1$-dimensional has a non-local geometry which is consistent with the experimental results of the Higgs experiments. In this letter we prove that the Higgs model in the $2+1$-dimensional has an algebraic structure of Geometrical Leibnitz type and that the Higgs field theory is a Geometrical Leibnitz field theory. In the case where the Higgs field theory is a Geometric Leibnitz field theory, the Higgs model is constructed, and we show that it obeys the Higgs formula. In particular, we compute the $2+1$-dimensional Higgs model in the $2+1$-dimensional Geometrical Leibnitz field theory and it is shown to be a Geometric Leibnitz field theory.