We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of d, N × N matrices invariant under the adjoint action of the symmetric group S_N. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group.

中文翻译：

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计量排列不变矩阵量子力学：路径积分

我们给出了规范有限群的量子力学配分函数的路径积分构造。我们的构造给出了在对称群S _N的伴随作用下不变的d、N × N矩阵系统的量化。该方法对于任何离散群体都是通用的。对于谐振子系统，即对于非相互作用的情况，配分函数由 Molien-Weyl 公式乘以零点能量贡献给出。我们进一步将结果推广到在规范组的任意表示下进行变换的非方和复矩阵系统。