基本对偶、量子对偶和拓扑对偶不变性理论
The Theory of Fundamental Duality, Quantum Dualiton and Topological Dual Invariance
摘要：
基本二元性是指两个不可约的、异质的、相互对立又相互补充的原理。量子力学中的互补原理也受到玻尔的赞扬。众所周知，这个重要的概念出现在我们的物理宇宙中的很多地方，但是严格的数学定义和物理理论还没有以正式的方式发展。本文建立了基本对偶的一种形式，并研究了它的各种性质和定理。其中最有意义的结果之一是建立了对偶不变性与拓扑不变性之间的关系，并发现拓扑Chern-Simons形式是对偶不变性作用。最后，我们应用对偶性的概念研究了对偶态的振荡，并预言了对偶子的一种新的理论态物质，即对偶场的粒子二次量子化激发。这种新的奇异准粒子态有望对粒子物理学和凝聚态物理产生影响。
英文摘要：
Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important concept is known to appear in a lot of places in our physical universe, however a rigorous mathematical definition and physics theory has not yet ever developed in a formal way. In this paper, we establish a formalism for fundamental duality and study its various properties and theorems. One of the most profound results is that we establish a relation between dual invariance and topological invariance, and we find that the topological Chern-Simons form is a dual invariant action. Finally we apply the concept of duality to study dual state oscillation, and predict a theoretical new matter of state of dualiton, which is the particle excitation of the dual field by second quantization. This new exotic quasi-particle state is expected to have an impact in particle physics and condensed matter physics.
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