What is a commmutator?

Answer 1

A commutator is a mathematical concept used primarily in algebra and quantum mechanics. In the context of group theory, it measures the extent to which two elements fail to commute, defined as ([a, b] = ab - ba) for elements (a) and (b). In quantum mechanics, commutators are used to express the uncertainty principle and the relationship between observables, such as position and momentum. They play a crucial role in understanding the structure of algebraic systems and the behavior of quantum systems.