On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states
On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states
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关于 OSp(1/2) 相干态下的超辛齐次超空间
DOI：
10.1063/1.530242
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
A. M. E. Gradechi
中科院分区：
文献类型：
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作者：
A. M. E. Gradechi
本文将Onofri和Perelomov的相干态方法推广到最近引入的OSp（1/2）相干态。后者被证明是由超辛超流形的点参数化的，即OSp（1/2）/U（1）齐次超空间，通过展示相应的等变超矩映射，它清楚地与OSp（1/2）的超余伴随轨道相一致。此外，这个超流形被证明是罗斯坦的超辛超流形的一个非平凡的例子。更精确地说，它的超辛结构完全由SU（1，1）-不变（但不相关）的Kahler 2-形式和单位圆盘上的Kahler度量决定。这个结果导致了超卡勒超流形和超卡勒超势的概念的定义，前者的几何结构被编码到后者。
In this work Onofri and Perelomov’s coherent states methods are extended to the recently introduced OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely, the OSp(1/2)/U(1) homogeneous superspace, which is clearly identified with a supercoadjoint orbit of OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein’s supersymplectic supermanifolds. More precisely, it is shown that its supersymplectic structure is completely determined in terms of SU(1,1)‐invariant (but unrelated) Kahler 2‐form and Kahler metric on the unit disc. This result leads to the definition of the notions of a super‐Kahler supermanifold and a super‐Kahler superpotential, the geometric structure of the former being encoded into the latter.