论文标题
Fock太空二元性
Fock space dualities
论文作者
论文摘要
在第二次量化的情况下，重新制定了由于经典群体的双重作用和某些非缔合代数在对称或交替张量的空间上引起的一般定理，并讨论了原子和核物理学的熟悉示例。详细处理正交 - 正交双重性的特殊情况。结果表明，就像半个多世纪前的舵手在符号成绩二元双重性的类似情况下一样，人们可以基于正交性偶性定理的证明，而精确的表征是通过对角色进行分析的指示来进行分析的双重相关类别的等价类别之间的相关性，并且是对等值的等价类别之间的相关性。介绍了用于描述正交谎言代数的不可减至表示等效类别的年轻图。数字反射的属性在正交谎言代数之间的双重关系中，对伴侣之间几乎完美的对称性的图片证实了数字。
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.
