非对易引力、"无附加条件“量子经典对偶性和宇宙学常数之谜
Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle
摘要：
应该存在一种不涉及外部经典时空流形的量子力学的重新表述。这样的重新表述可以使用非交换微分几何的语言来实现。由此得出的一个结论是，一个质量远大于普朗克质量的相对论性粒子的“弱量子、强引力”动力学与另一个质量远小于普朗克质量的粒子的“强量子、弱引力”动力学是对偶的。这两个粒子的质量彼此成反比，它们质量的乘积等于普朗克质量的平方。这种对偶性解释了观测到的宇宙学常数的值，也解释了为什么这个值不为零，但在普朗克单位下非常小。
英文摘要：
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.
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