Gauge dependence and Dyson Schwinger equations II

我们的目标是理解离壳绿色函数的规范不变性。现代代数代数方法允许通过研究Hopf代数中的余理想来解决这个问题。绿色功能出现的解决方案不动点方程的Hochschild上同调这些代数和定义以这种方式戴森Schwinger方程。我们集中我们的研究4和更高的n点函数，与外部鬼，规范和物质领域，在协变线性和非线性规范和不同的重整化方案。 使用拉格朗日乘子，这样的问题也可以研究领域的理论在更高的偶数维和背景下的运营商产品expansions.We将调查跨维度的普遍性质，如建议的1/N的扩展，回答问题的关系共形场理论，自举和a-定理。

We aim at an understanding of gauge invariance in off-shell Green functions.Modern algebraic algebraic methods allow to attack the problem via the study of co-ideals in Hopf algebras. Green functions appear as solutions to fixed point equations in the Hochschild cohomology of these algebras and define in this manner the Dyson Schwinger equations. We concentrate our study on 4- and higher n-point functions, with external ghost-, gauge- and matter fields, in covariant linear and non-linear gauges and varying renormalization schemes. Using Lagrange multipliers such questions can also be studied for field theories in higher even dimensions and in the context of the operator product expansions.We will investigate universal properties across dimensions of such theories as suggested by the 1/N expansion, answering questions on relations to conformal field theory, the bootstrap and the a-Theorem.