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Super Ginsparg–Wilson algebra and Dirac operator on the super fuzzy Euclidean hyperboloid EAdSF(2|2)
International Journal of Modern Physics A ( IF 1.4 ) Pub Date : 2020-11-11 , DOI: 10.1142/s0217751x20501961
M. Lotfizadeh 1
Affiliation  

In this paper, we construct super fuzzy Dirac and chirality operators on the super fuzzy Euclidean hyperboloid [Formula: see text] in-instanton and no-instanton sectors. Using the super pseudo-projectors of the noncompact first Hopf fibration, we construct the Ginsparg–Wilson algebra in instanton and no-instanton sectors. Then, using the generators of this algebra, we construct pseudo super-Dirac and chirality operators in both sectors. We also construct pseudo super-Dirac and chirality operators corresponding to the case in which our theory includes gauge fields. We show that they have correct commutative limit in the limit case when the noncommutative parameter [Formula: see text] tends to infinity.

中文翻译:

超级模糊欧几里得双曲面 EAdSF(2|2) 上的超级 Ginsparg-Wilson 代数和狄拉克算子

在本文中,我们在超模糊欧几里得双曲面[公式:见正文] in-instanton 和 no-instanton 扇区上构造了超模糊 Dirac 和手性算子。使用非紧第一 Hopf 纤维化的超级伪投影,我们在瞬时和非瞬时扇区中构造 Ginsparg-Wilson 代数。然后,使用这个代数的生成器,我们在两个扇区中构造伪超狄拉克和手性算子。我们还构造了与我们的理论包括规范场的情况相对应的伪超狄拉克和手性算子。当非交换参数[公式:见文本]趋于无穷大时,我们证明了它们在极限情况下具有正确的交换极限。
更新日期:2020-11-11
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