Research for ideal gas with fractional statistics

1997年，我们研究了IIB型矩阵模型的分析。超弦理论一直被称为“万物理论”，它可以统一包括引力在内的所有相互作用，但没有人不能研究它的非微扰方面。1996年秋，KEK的H.Kawai等人提出了IIB型超弦的构造性模型。通过分析这个模型，我们原则上可以解决许多难题，例如为什么我们生活在四维空间中，或者为什么宇宙常数正在消失。我和H.Kawai的团队一起研究了这个问题，并展示了我们的时空是如何从该模型中出现的。在这个模型中，由于对角分量成为时空坐标，我们可以通过积分非对角分量并得到这些对角分量的有效作用来讨论时空的性质。我们确实得到了这个有效作用，并讨论了这个作用的几个性质。由于这个模型仍然很难解决，我们不能确定，但我们已经展示了我们的四维时空如何出现的一些可能性。

We have studied analysis of type IIB matrix model in 1997. Superstring theory has been known as a "theory of everything" which can unify all interactions including gravity but nobody could not investigate its non-perturbative aspects of it. In the fall of 1996 H.Kawai et.al.at KEK proposed a constructive model of type IIB superstring. By analysing this model we can in principle solve many difficult problems such as why we are live in four dimensions or why the cosmological constant is vanishing.I investigated this problem together with the group of H.Kawai and have shown how our space-time appears from the model. Since the diagonal components become space-time coodinates in this model, we can discuss the properties of space-time by integrating the off diagonal components and obtaining the effective action for these diagonal components. We have indeed obtained the effective action and discussed several properties of this action. Since the model is still difficult to solve, we can not be sure but we have shown some possibilities how our four dimensional space-time appears.