论文标题

旋转器在非交通时空上的传播:形式和有效方法的等效性

Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach

论文作者

Ćirić, Marija Dimitrijević, Konjik, Nikola, Samsarov, Andjelo

论文摘要

某些非交通性(NC)理论具有某种类型的双重性,这些双重性是隐含在其结构内的。在本文中,我们建立了此类的另一个例子。更准确地说,我们表明,非公共性u(1)量表理论耦合到NC标量字段以及Reissner Nordstrom(RN)类型的经典几何形状在运动方程级别完全等效到交换性u(1)的运动级别,从而使u(1)的理论相对于上的质量量表和阶级的背景,从而与阶级的背景相差不同。新的(有效)度量是从RN度量中获得的,通过打开其他非散布R-PHI组件。使用它们描述的两种理论和物理系统之间的二元性,我们制定了一种有效的方法,可以在RN类型的弯曲背景下使用具有牢固的非交通性结构的曲面背景进行旋转1/2个字段的动力学。与此相比,我们还通过研究半经典理论,以更正式的方式研究自旋1/2场的动力学,该理论描述了NC U(1)量规场与NC Spin 1/2场相结合,并具有重力,但是经典地对待。在利用Seiberg Witten地图以根据其相应的交换自由度来编写NC旋转器和NC量规场,我们发现在形式方法中获得的费米昂运动的运动方程与使用非公示性二元性的有效方法中获得的运动方程完全恰好相吻合。然后,我们使用这些结果来分析运动方程方程解决方案的稳定性和相关的超级缩影问题,与具有全面的非共同结构的RN时空相关。

Some noncommutative (NC) theories posses a certain type of dualities that are implicitly built within their structure. In this paper we establish still another example of this kind. More precisely, we show that the noncommutative U(1) gauge theory coupled to a NC scalar field and to a classical geometry of the Reissner Nordstrom (RN) type is completely equivalent at the level of equations of motion to the commutative U(1) gauge theory coupled to a commutative scalar field and to a classical geometry background, different from the starting RN background. The new (effective) metric is obtained from the RN metric by switching on an additional nonvanishing r-phi component. Using this duality between two theories and physical systems they describe, we formulate an effective approach to studying a dynamics of spin 1/2 fields on the curved background of RN type with an abiding noncommutative structure. As opposed to that, we also study the dynamics of spin 1/2 fields in a more formal way, by studying the semiclassical theory which describes the NC U(1) gauge field coupled with NC spin 1/2 field and also with gravity which is however treated classically. Upon utilising the Seiberg Witten map in order to write the NC spinor and NC gauge fields in terms of their corresponding commutative degrees of freedom, we find that the equation of motion for the fermion field obtained within the formal approach exactly coincides with the equation of motion obtained within the effective approach that utilises noncommutative duality. We then use these results to analyze the problem of stability of solutions of the equations of motion and the associated issue of superradiance, as related to fermions in RN spacetime with an allpervasive noncommutative structure.

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