矩阵模型与椭圆曲线
Matrix Model and Elliptic Curve
摘要：
研究了非零费米子场下IKKT型约化矩阵模型的解。一个建议是，我们的宇宙是由有理数，而不是一个连续。为了证实这个提议，简化的杨-米尔斯方程被写成椭圆曲线的形式。解的正规化一般可以用Weierstrass函数表示，或者在3-膜的情况下可以用Dedekind函数表示。提出了一种在矩阵模型中定义引力场的方法，并对宇宙学常数作了新的解释。系统的（第一）量子化是在非对易几何的框架内完成的。
英文摘要：
Solution to the reduced matrix model of IKKT type is studied with non-zero fermion fields. A suggestion is made that our universe is made of rational numbers rather than being a continuum. To substantiate this proposal, the reduced Yang-Mills equation is written in the form of an elliptic curve. The normalization of the solution can be expressed in terms of the Weierstrass function generically or in terms of the Dedekind function in the case of 3-brane. A way to define the gravitational field in the matrix model is proposed with some new interpretation of the cosmological constant. The (first) quantization of the system is done within the framework of non-commutative geometry.
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