Rota-Baxter代数的非交换Bohnenblust-Spitzer恒等式解Bogoliubov递归
A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
摘要：
Bogoliubov递推是微扰量子场论重整化过程中出现的一个特殊过程。它提供了收敛表达式，否则发散积分。我们在这里开发的非交换Rota-Baxter代数的功能标识的理论，这是编码，除其他外，这一过程中的背景下，康纳斯-Kreimer的霍普夫代数的重整化。我们的结果推广了交换Rota-Baxter代数的经典Spitzer型恒等式的Cartier-Rota理论。在经典的交换情形下，这些恒等式可以理解为从对称函数理论中导出。在这里，我们表明，一个类似的性质持有非交换Rota-Baxter代数。也就是说，我们表明，在非交换设置功能的身份可以从非交换对称函数的理论。李幂等元，特别是Dynkin幂等元在这个过程中起着至关重要的作用。他们的行动对亲幂幺群，如那些微扰重整化的详细描述的方式。
英文摘要：
The Bogoliubov recursion is a particular procedure appearing in the process of renormalization in perturbative quantum field theory. It provides convergent expressions for otherwise divergent integrals. We develop here a theory of functional identities for noncommutative Rota-Baxter algebras which is shown to encode, among others, this process in the context of Connes-Kreimer's Hopf algebra of renormalization. Our results generalize the seminal Cartier-Rota theory of classical Spitzer-type identities for commutative Rota-Baxter algebras. In the classical, commutative, case, these identities can be understood as deriving from the theory of symmetric functions. Here, we show that an analogous property holds for noncommutative Rota-Baxter algebras. That is, we show that functional identities in the noncommutative setting can be derived from the theory of noncommutative symmetric functions. Lie idempotents, and particularly the Dynkin idempotent play a crucial role in the process. Their action on the pro-unipotent groups such as those of perturbative renormalization is described in detail along the way.
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