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 most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“Wonder is the foundation of all philosophy; research, the progress; ignorance, the end. There is, by heavens, a strong and generous kind of ignorance that yields nothing, for honour and courage, to knowledge: an ignorance to conceive which needs no less knowledge than to conceive knowledge.”
—Michel de Montaigne (1533–1592)
“Therefore doth heaven divide
The state of man in divers functions,
Setting endeavor in continual motion,
To which is fixed, as an aim or butt,
Obedience; for so work the honeybees,
Creatures that by a rule in nature teach
The act of order to a peopled kingdom.”
—William Shakespeare (1564–1616)