分数粗粒方法中带电轻子的反常g因子
Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
摘要：
在这项工作中，我们调查方面的电子，μ子和τ旋磁比（g因子）在一个分数粗粒度的情况下，通过采用修改的黎曼刘维（MRL）分数微积分。我们指出的可能性映射到一个理论参数，占分数的物质的g-因子的实验值，而不计算高阶QED计算。我们希望了解（g-2）的值是否可以追溯到时空的分形性。由狄拉克方程产生的g=2的实验值和理论值之间的差异的理由是带电轻子相互作用的复杂性，认为它们是赝粒子，并被相互作用和介质“装扮”。逐步地，我们建立了一个分数阶狄拉克方程的分数阶外尔方程，另一方面，制定专门的螺旋算子。从分数阶角动量代数出发，在粗粒度的情况下，我们计算出自旋算符的本征值。在标准电磁流的基础上，作为类比情形，我们写出了一个分数拉格朗日密度，其中电磁场与特殊带电轻子的耦合最小。然后，我们研究了分数规范的不变性对称性，制定协变分数导数和提出旋量场变换。最后，通过取分数阶Dirac方程的非相对论性区域，得到分数阶Pauli方程，并由此得到分数阶g因子的显式表达式，与实验CODATA值进行了比较。我们的主张是，不同的轻子种类必须通过经历不同的分数来探测时空，一旦后者可能与不同家族与介质的有效相互作用相关联。
英文摘要：
In this work, we investigate aspects of the electron, muon and tau gyromagnetic ratios (g-factor) in a fractional coarse-grained scenario, by adopting a Modified Riemann-Liouville (MRL) fractional calculus. We point out the possibility of mapping the experimental values of the specie's g-factors into a theoretical parameter which accounts for fractionality, without computing higher-order QED calculations. We wish to understand whether the value of (g-2) may be traced back to a fractionality of space-time.The justification for the difference between the experimental and the theoretical value g=2 stemming from the Dirac equation is given in the terms of the complexity of the interactions of the charged leptons, considered as pseudo-particles and "dressed" by the interactions and the medium. Stepwise, we build up a fractional Dirac equation from the fractional Weyl equation that, on the other hand, was formulated exclusively in terms of the helicity operator. From the fractional angular momentum algebra, in a coarse-grained scenario, we work out the eigenvalues of the spin operator. Based on the standard electromagnetic current, as an analogy case, we write down a fractional Lagrangian density, with the electromagnetic field minimally coupled to the particular charged lepton. We then study a fractional gauge-like invariance symmetry, formulate the covariant fractional derivative and propose the spinor field transformation. Finally, by taking the non-relativistic regime of the fractional Dirac equation, the fractional Pauli equation is obtained and, from that, an explicit expression for the fractional g-factor comes out that is compared with the experimental CODATA value. Our claim is that the different lepton species must probe space-time by experiencing different fractionalities, once the latter may be associated to the effective interactions of the different families with the medium.
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