如何安装反括号
How to quantize the antibracket
摘要：
Poisson李代数变形（类）的唯一性早已被人们所接受。实际上，它是错误的，因为它的有效性取决于生成泊松李代数Po（2n）的函数类：它对多项式是真的，但对洛朗多项式是假的。我们证明了与李超代数Po（2n）不同，|m），它的商模中心，李超代数H（2n| m）具有特殊的额外变形|m）=（2| 2）且仅限于此超维。我们将这个结果与反括号（也称为Schouten或Buttin括号）变形的完整描述联系起来。泊松代数在福克空间中的变形（量子化的结果）的表示与对易关系的李代数作用的最简单的空间一致。这种重合对于李超代数来说是不必要的
英文摘要：
The uniqueness of (the class of) deformation of Poisson Lie algebra has long been a completely accepted folklore. Actually, it is wrong as stated, because its validity depends on the class of functions that generate Poisson Lie algebra, Po(2n): it is true for polynomials but false for Laurent polynomials. We show that unlike the Lie superalgebra Po(2n|m), its quotient modulo center, the Lie superalgebra H(2n|m) of Hamiltonian vector fields with polynomial coefficients, has exceptional extra deformations for (2n|m)=(2|2) and only for this superdimension. We relate this result to the complete description of deformations of the antibracket (also called the Schouten or Buttin bracket). The representation of the deform (the result of quantization) of the Poisson algebra in the Fock space coincides with the simplest space on which the Lie algebra of commutation relations acts. This coincidence is not necessary for Lie superalgebras
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