论文标题
在l $ _ \ infty $ poisson仪表理论的结构
On the L$_\infty$ structure of Poisson gauge theory
论文作者
论文摘要
Poisson仪表理论是完整非交通仪理论的半古典限制。在这项工作中，我们构建了一个l $ _ \ infty^{full} $代数，该代数既控制量规对称的动作和泊松仪理论的动力学。我们得出了最小的非散布$ \ ell $ - 支架，并证明它们满足了相应的同拷贝关系。一方面，它提供了L $ _ \ infty $代数的新的明确的非平凡示例。另一方面，它可以用作引导完整的非共同规格理论的起点。这种理论的前几个括号是在文本中明确构建的。此外，我们还表明，相对于外部代数上截断的产品，$ \ ell $ - 支架在l $ _ \ infty^{full} $上的派生属性仅对规范的非交换性得到满足。通常，l $ _ \ infty^{full} $没有p $ _ \ infty $代数的结构。
The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory. We derive the minimal set of non-vanishing $\ell$-brackets and prove that they satisfy the corresponding homotopy relations. On the one hand, it provides new explicit non-trivial examples of L$_\infty$ algebras. On the other hand, it can be used as a starting point for bootstrapping the full non-commutative gauge theory. The first few brackets of such a theory are constructed explicitly in the text. In addition we show that the derivation properties of $\ell$-brackets on L$_\infty^{full}$ with respect to the truncated product on the exterior algebra are satisfied only for the canonical non-commutativity. In general, L$_\infty^{full}$ does not have a structure of P$_\infty$ algebra.
