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arXiv quant-ph/0012099quant-phcond-mathep-th
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SU的相干态(3)

Coherent States For SU(3)

Manu Mathur, Diptiman Sen

摘要:

我们用六个玻色子产生和湮灭算符定义了SU(3)的相干态。这些相干态的特征是明确的六个复数的约束。对于完全对称表示(n,0)和(0,m),只需要三个玻色子算子。对于混合表示(n,m),需要所有六个运算符。相干态提供了一种恒等式的解决方案,满足连续性,并具有各种群论性质。我们引入了SU(3)群的一个显式参数化和相应的积分测度。最后,我们讨论了一个问题的路径积分形式,其中的哈密顿量是一个功能的SU(3)运营商在每个网站。

英文摘要:

We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n,0) and (0,m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site.

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