Effective QED actions: Representations, gauge invariance, anomalies and mass expansions
Effective QED actions: Representations, gauge invariance, anomalies and mass expansions
复制标题
有效的 QED 动作：表示、规范不变性、异常和质量膨胀
DOI：
10.1103/physrevd.57.7444
复制
发表时间：
1997
影响因子：
5
通讯作者：
D. Seminara
中科院分区：
文献类型：
--
作者：
S. Deser;L. Griguolo;D. Seminara
我们分析并给出了带电费米子产生的有效阿贝尔矢量规范场作用量的显式表示，特别注意了奇数维中的热区域，在奇数维中可能存在谱不对称。通过ζ函数正则化，我们证明了在任何温度下，对于任意数量的费米子，在通常的反常代价下，小规范不变性和大规范不变性都是不变的：螺旋度(宇称)不变性将在偶(奇)维中消失，而在后者中，甚至在零质量下也是如此。规范不变性根据携带新颖的大规范不变信息的完整概念，规定了作用量的一个非常一般的“傅立叶”表示。我们证明了大的(不同于小的)变换和它们的Ward恒等式不是微扰保序的，并阐明了(适当重新定义的)Chern-Simons项在这方面的作用。从无质量热核的作用量的一个强有力的表示，我们能够得到严格的规范不变展开式，无论是小的和大的费米子质量，其单独的奇偶部分宇称奇偶部分在任意维度。该表象还显示了有限重整化模糊度的非微扰起源和它的物理分辨率，要求在无限质量下解耦。最后，我们通过对三维情形中场组态的一些物理例子的有效作用的显式计算来说明这些一般结果，其中我们关于有限温度效应的结论可能具有物理意义。非阿贝尔结果将单独公布。
We analyze and give explicit representations for the effective Abelian vector gauge field actions generated by charged fermions with particular attention to the thermal regime in odd dimensions, where spectral asymmetry can be present. We show, through ζ-function regularization, that both small and large gauge invariances are preserved at any temperature and for any number of fermions at the usual price of anomalies: helicity (parity) invariance will be lost in even (odd) dimensions, and in the latter even at zero mass. Gauge invariance dictates a very general “Fourier” representation of the action in terms of the holonomies that carry the novel, large gauge-invariant, information. We show that large (unlike small) transformations and hence their Ward identities are not perturbative order-preserving, and clarify the role of (properly redefined) Chern-Simons terms in this context. From a powerful representation of the action in terms of massless heat kernels, we are able to obtain rigorous gauge-invariant expansions, for both small and large fermion masses, of its separate parity even and odd parts in arbitrary dimension. The representation also displays both the nonperturbative origin of a finite renormalization ambiguity and its physical resolution by requiring decoupling at infinite mass. Finally, we illustrate these general results by explicit computation of the effective action for some physical examples of field configurations in the three-dimensional case, where our conclusions on finite temperature effects may have physical relevance. Non-Abelian results will be presented separately.