论文标题
Kapranov的$ L_ \ Infty $结构，Fedosov的Star Products和Kähler歧管上的一环bv量化
Kapranov's $L_\infty$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds
论文作者
论文摘要
我们研究了Kähler歧管上的量化方案，并关联了几个有趣的结构。我们首先在Kähler歧管$ x $上构建了Fedosov的Star产品，作为Kapranov的$ L_ \ Infty $ -Algebra结构的量化。然后，我们研究了与这些恒星产品相关的Batalin-Vilkovisky（BV）量化。一个了不起的特征是它们都是一环准确的，这意味着与图形相关的Feynman权重都消失了。这导致了代数指数的DE RHAM共同体学中简洁的科链级公式。
We study quantization schemes on a Kähler manifold and relate several interesting structures. We first construct Fedosov's star products on a Kähler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we investigate the Batalin-Vilkovisky (BV) quantizations associated to these star products. A remarkable feature is that they are all one-loop exact, meaning that the Feynman weights associated to graphs with two or more loops all vanish. This leads to a succinct cochain level formula in de Rham cohomology for the algebraic index.
