标题： 利用泛函积分和微扰计算的异常研究 显示英文标题

标题： A study of anomalies using functional integration and perturbative calculations

摘要： 我们提出了两种涉及反常现象的研究路径。 首先，我们利用泛函积分回顾了经典和量子对称性守恒背后的机制。这一讨论阐明了量子反常的条件，正如手征理论所承认的那样。 接着，我们阐明了当所有场都被量子化时规范反常抵消的主题。这种结果要求玻色子测度具有规范不变性，因此我们的第一个目标是在藤川方法中证明这种不变性。 其次，我们利用隐式正则化研究了费米子微扰振幅中的反常现象。单轴三角形函数的基础讨论奠定了这一分析的基础，引入了处理单轴盒子所需的要素。在组织它们的数学结构时，我们强调了涉及手征矩阵的迹的作用。选择它们的具体表达方式会影响对称性破坏的位置，这与积分的线性相关。 幂计数和张量结构暗示了与动量歧义相关的表面项的存在。我们给出了结果而不计算这些表面项。 在这种中立的观点下，我们探讨了不同规则下可能实现的结果。 显示英文摘要

摘要： We present two lines of investigation involving anomalies. First, we review mechanisms behind the classical and quantum conservation of symmetries using functional integration. This discussion clarifies conditions for quantum violations, as acknowledged in chiral theories. Then, we elucidate the subject of gauge anomaly cancellation when all fields are quantized. Such an outcome requires gauge invariance of the bosonic measure, so our first object is proving this invariance within Fujikawa's approach. Second, we investigate anomalies in fermionic perturbative amplitudes using Implicit Regularization. The discussion of the single-axial triangle fundaments this analysis, bringing the elements necessary to approach the single-axial box. When organizing their mathematical structure, we highlight the role of traces involving the chiral matrix. Choosing a specific expression for them reflects on the position of symmetry violations, which has implications regarding the linearity of integration. Power counting and tensor structure imply the presence of surface terms related to momenta ambiguities. We present the results without computing these surface terms. In this neutral perspective, we explore possibilities achieved under different prescriptions.