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:
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)
“I believe that the mind can be permanently profaned by the habit of attending to trivial things, so that all our thoughts shall be tinged with triviality. Our very intellect shall be macadamized, as it were,—its foundation broken into fragments for the wheels of travel to roll over.”
—Henry David Thoreau (1817–1862)
“Do we have to talk in order to agree or agree in order to talk?”
—José Bergamín (1895–1983)