SU的预势公式（3）格点规范理论
Prepotential formulation of SU(3) lattice gauge theory
摘要：
用SU（3）预势谐振子重新表述了SU（3）格点规范理论。这种重新表述扩大了$SU(3)\otimes U(1) \otimes U(1)$规范不变性，在这种规范不变性下，前势算子像物质场一样变换。本文证明了SU（3）格点规范理论的Hilbert空间等价于满足一定色不变Sp（2，R）约束的前势形式的Hilbert空间。求解这些Sp（2，R）约束的SU（3）不可约预势算子在每个格点上用SU（3）规范不变顶点算子构造SU（3）规范不变Hilbert空间.利用这些SU（3）不可约预势算符重构了电场和链算符。我们表明，所有的SU（3）曼德尔维约束成为本地的，并采取非常简单的形式在这种方法。我们还讨论了所有可能的线性无关的SU（3）环态的构造，解决了Mandeltek约束。这些技巧可以很容易地推广到SU（N）。
英文摘要：
The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential harmonic oscillators. This reformulation has enlarged $SU(3)\otimes U(1) \otimes U(1)$ gauge invariance under which the prepotential operators transform like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to be equivalent to the Hilbert space of the prepotential formulation satisfying certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential operators which solve these Sp(2,R) constraints are used to construct SU(3) gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge invariant vertex operators. The electric fields and the link operators are reconstructed in terms of these SU(3) irreducible prepotential operators. We show that all the SU(3) Mandelstam constraints become local and take very simple form within this approach. We also discuss the construction of all possible linearly independent SU(3) loop states which solve the Mandelstam constraints. The techniques can be easily generalized to SU(N).
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