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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. Thisimportant concept is known to appear in a lot of places in our physicaluniverse, however a rigorous mathematical definition and physics theory has notyet ever developed in a formal way. In this paper, we establish a formalism forfundamental duality and study its various properties and theorems. One of themost profound results is that we establish a relation between dual invarianceand topological invariance, and we find that the topological Chern-Simons formis a dual invariant action. Finally we apply the concept of duality to studydual state oscillation, and predict a theoretical new matter of state ofdualiton, which is the particle excitation of the dual field by secondquantization. This new exotic quasi-particle state is expected to have animpact in particle physics and condensed matter physics.

The Theory of Fundamental Duality, Quantum Dualiton and Topological Dual Invariance