Fock空间对偶
Fock space dualities
摘要：
在二次量子化的背景下，重新表述了Howe关于经典群和非结合代数在对称或交错张量空间上的对偶作用的一般定理，并讨论了原子核物理中常见的例子.特殊情况下的正交正交对偶的详细处理。它表明，就像它是由赫尔墨斯在半个多世纪前在类似的情况下辛辛对偶，人们可以根据证明的正交正交对偶定理和精确表征之间的关系的等价类的对偶相关的不可约表示的计算字符相结合的分析表示的反射。引入了用于描述正交李代数不可约表示等价类的Young图。正交李代数之间的对偶关系中的数非守恒部分的反射的性质证实了伙伴之间的几乎完美对称的图像。
英文摘要：
A general theorem due to Howe of dual action of a classical group and a certain non-associative algebra on a space of symmetric or alternating tensors is reformulated in a setting of second quantization, and familiar examples in atomic and nuclear physics are discussed. The special case of orthogonal-orthogonal duality is treated in detail. It is shown that, like it was done by Helmers more than half a century ago in the analogous case of symplectic-symplectic duality, one can base a proof of the orthogonal-orthogonal duality theorem and a precise characterization of the relation between the equivalence classes of the dually related irreducible representations on a calculation of characters by combining it with an analysis of the representation of a reflection. Young diagrams for the description of equivalence classes of irreducible representations of orthogonal Lie algebras are introduced. The properties of a reflection of the number non-conserving part in the dual relationship between orthogonal Lie algebras corroborate a picture of an almost perfect symmetry between the partners.
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