标题： 二维奇泡、四维三角形以及二维引力费米振幅中的爱因斯坦和外尔反常：反常线性积分破坏的作用 显示英文标题

标题： The Odd 2D Bubbles, 4D Triangles, and Einstein and Weyl Anomalies in 2D Gravitational Fermionic amplitudes: The Role of Breaking Integration Linearity for Anomalies

摘要： 我们研究了在处理发散问题的另一种策略中定义的绿色函数之间的关系，该方法也称为隐正则化方法（IREG）：数学内容（发散和有限部分）在整个计算结束前将保持不变。 发散部分将通过不含物理量的标准对象来组织。 相比之下，有限部分被投影到一类具有良好行为的函数类中，这些函数携带所有振幅的物理内容。 这些关系出现在偶数时空维度的费米子振幅中，在这里反常张量与有限振幅相连，就像二维和四维中的气泡和三角形一样。 这些张量依赖于表面项，其非零值来源于有限振幅的一致性要求，与积分的线性和唯一性相关。 保持这些项意味着打破动量空间的齐次性，并在后续步骤中破坏Ward恒等式。 同时，消除它们允许同一个振幅有不止一种数学表达方式。 这是由于与涉及的Dirac迹相关的选择引起的。 无论是否存在发散，都不可能通过同时要求表面项消失和保持线性来满足所有对称性的推论。 随后，我们通过弯曲时空中的Weyl费米子的作用研究了D=1+1时空中的引力子传播的1-圈水平费米子修正。 在此背景下，会出现引力异常，并且所研究的振幅具有最高的二次发散度。 这需要大量的代数努力；然而，结论与非引力振幅一致。 在计算结束时，我们展示了如何通过施加于振幅的关系来确定发散部分的值。 显示英文摘要

摘要： We investigated Relations Among Green Functions defined in an alternative strategy for coping with the divergences, also called the Implicit Regularization Method (IREG): the mathematical content (divergent and finite) will remain intact until the calculations end. The divergent part will be organized through standardized objects free of physical quantities. In contrast, the finite part is projected in a class of well-behaved functions that carry all the amplitudes' physical content. That relations arise in fermionic amplitudes in even space-time dimensions, where anomalous tensors connect to finite amplitudes as in the bubbles and triangles in two and four dimensions. Those tensors depend on surface terms, whose non-zero values arise from finite amplitudes as requirements of consistency with the linearity of integration and uniqueness. Maintaining these terms implies breaking momentum-space homogeneity and, in a later step, the Ward identities. Meanwhile, eliminating them allows more than one mathematical expression for the same amplitude. That is a consequence of choices related to the involved Dirac traces. Independently of divergences, it is impossible to satisfy all symmetry implications by simultaneously requiring vanishing surface terms and linearity. Then we approach the 1-loop level fermionic correction for the propagation of the graviton in a space-time D=1+1 through the action of a Weyl fermion in curved space-time. In this context, gravitational anomalies arise, and the amplitudes investigated have the highest degree of divergence quadratic. That imposes a substantial algebraic effort; however, the conclusions are in agreement with the non-gravitational amplitudes. At the end of the calculations, we show how it is possible to fix the value of the divergent part through the relations imposed for amplitudes.