反Poisson几何中的语义、第二类约束与转换
Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry
摘要：
在退化的反Poisson流形上，考虑了Batalin-Vilkovisky（BV）算子Δ E的Khudaverdian几何形式.这种算子的特征（除了是格拉斯曼奇、幂零、二阶微分算子之外）是它将语义发送给语义。我们找到了任意坐标系下Δ E算子的一个局部公式。作为这一理论的一个重要应用，我们研究了具有反辛第二类约束的反辛流形上的Dirac反括号。我们证明了整个Dirac构造，包括相应的Dirac BV算子Δ_{E_D}，都是从扩张流形上的反辛第二类约束到第一类约束的转换而来的.
英文摘要：
We consider Khudaverdian's geometric version of a Batalin-Vilkovisky (BV) operator Δ_E in the case of a degenerate anti-Poisson manifold. The characteristic feature of such an operator (aside from being a Grassmann-odd, nilpotent, second-order differential operator) is that it sends semidensities to semidensities. We find a local formula for the Δ_E operator in arbitrary coordinates. As an important application of this setup, we consider the Dirac antibracket on an antisymplectic manifold with antisymplectic second-class constraints. We show that the entire Dirac construction, including the corresponding Dirac BV operator Δ_{E_D}, exactly follows from conversion of the antisymplectic second-class constraints into first-class constraints on an extended manifold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
