Mathematical Foundation of Topological Order
We know that group theory is the mathematical foundation of symmetry breaking orders. What is the mathematical foundation of topological order? The string-net condensation suggests that tensor category (or monoidal category) theory may be the mathematical foundation of topological order. Quantum operator algebra is a very important mathematical tool in studying topological orders. A subclass of toplogical order—Abelian topological order in two dimensions—can be classified by a K-matrix approach. Some also suggest that topological order is mathematically described by extended quantum symmetry.
Read more about this topic: Topological Order
Famous quotes containing the words mathematical, foundation and/or order:
“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)
“The most excellent and divine counsel, the best and most profitable advertisement of all others, but the least practised, is to study and learn how to know ourselves. This is the foundation of wisdom and the highway to whatever is good.... God, Nature, the wise, the world, preach man, exhort him both by word and deed to the study of himself.”
—Pierre Charron (1541–1603)
“When the book comes out it may hurt you—but in order for me to do it, it had to hurt me first. I can only tell you about yourself as much as I can face about myself.”
—James Baldwin (1924–1987)