多双子模拟中模空间度规的注意事项
Cautionary remarks on the moduli space metric for multi-dyon simulations
摘要：
我们对Diakonov和Petrov [arXiv：0704.3181]提出的一个双子约束模型的近似模空间度规进行了详细的数值研究。我们的研究结果强烈地表明，只有在足够低的密度下，对于少数的双子，这个度量是正定的-因此，在相当大的一部分位形空间中，它是一个有效的模空间度量。这对在该模型中通过集体坐标上的无限制积分获得的结果造成了很大的限制。它还表明，集体坐标之间的强相关性将是必不可少的一个双子模型的物理内容，这可以表现出一个合适的模拟算法。
英文摘要：
We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at sufficiently low density this metric is positive definite - and, therefore, a valid moduli space metric - throughout a considerable part of configuration space. This poses strong limitations on results obtained by an unrestricted integration over collective coordinates in this model. It also indicates that strong correlations between collective coordinates will be essential for the physical content of a dyon model, which could be exhibited by a suitable simulation algorithm.
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