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arXiv 2003.06819hep-th
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一阶Yang-Mills理论的相容性条件

Consistency Conditions for the First-Order Formulation of Yang-Mills Theory

F T Brandt, J Frenkel, S Martins-Filho, D G C McKeon

备注：
15 pages, 6 figures
发表信息：
Phys. Rev. D 101, 085013 (2020)
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摘要：

我们研究了杨-米尔斯理论的一阶公式的自洽性。通过比较生成泛函$Z$之前和之后整合出的附加字段$F^a_{μν}$，我们得出了一组结构的身份，必须满足的格林函数在所有的订单。这些恒等式在任何维都成立，不同于通常的沃德恒等式，并且是一阶形式主义的内部一致性所必需的。他们将涉及场$F^a_{μν}$的格林函数与包含胶子强度张量$f^a_{μν}$的二阶格林函数联系起来。特别地，这样的标识可以提供附加字段$F^a_{μν}$的简单物理解释。

英文摘要：

We examine the self-consistency of the first-order formulation of the Yang-Mills theory. By comparing the generating functional $Z$ before and after integrating out the additional field $F^a_{μν}$, we derive a set of structural identities that must be satisfied by the Green's functions at all orders. These identities, which hold in any dimension, are distinct from the usual Ward identities and are necessary for the internal consistency of the first-order formalism. They relate the Green's functions involving the fields $F^a_{μν}$, to Green's functions in the second-order formulation which contain the gluon strength tensor $f^a_{μν}$. In particular, such identities may provide a simple physical interpretation of the additional field $F^a_{μν}$.

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