论文标题
在Razamat的$ A_2 $和$ A_3 $内核身份
On Razamat's $A_2$ and $A_3$ kernel identities
论文作者
论文摘要
在最新的超量子量子场理论的工作中，Razamat到达了一个新的且引人注目的角色的椭圆内核身份：它们仅与root Systems $ a_2 $和$ a_3 $相关，并且没有耦合类型参数\ cite \ cite {ra18}。相关的2-和3变量的哈密顿量是分析差异操作员，并且内核函数是由椭圆γ函数构建的。 Razamat为这些身份的有效性提供了令人信服的证据，并在功率系列扩展中将其检查为一定顺序。本文主要涉及这些身份的分析证明。更具体地说，我们提供了$ A_2 $椭圆情况和$ A_3 $双曲线案例的身份的完整证明，并考虑了几种专业。我们还讨论了内核身份可能对涉及汉密尔顿人常见特征向量和与核函数相关的整体操作员的含义。
In recent work on superconformal quantum field theories, Razamat arrived at elliptic kernel identities of a new and striking character: They relate solely to the root systems $A_2$ and $A_3$ and have no coupling type parameters \cite{Ra18}. The pertinent 2- and 3-variable Hamiltonians are analytic difference operators and the kernel functions are built from the elliptic gamma function. Razamat presented compelling evidence for the validity of these identities, and checked them to a certain order in a power series expansion. This paper is mainly concerned with analytical proofs of these identities. More specifically, we furnish a complete proof of the identities for the $A_2$ elliptic case and for the $A_3$ hyperbolic case, and consider several specializations. We also discuss the implications the kernel identities might have for a Hilbert space scenario involving common eigenvectors of the Hamiltonians and the integral operators associated with the kernel functions.
