Commutator
- Modern Physics -
Quantum Mechanics Dictionary
Definition
An operator concept used to encode measurable quantities, transformations, or noise processes in a quantum model. It governs how outcome statistics and transformations are computed from state vectors or density operators. It does not guarantee physical relevance unless required properties such as positivity and normalization are satisfied.
Commutator
- Pure Mathematics -
Algebra Dictionary
Definition
A binary operation that measures the failure of two elements to commute. In groups it is often defined by [a,b] = a^{-1} b^{-1} a b (or equivalently a b a^{-1} b^{-1} depending on convention); in Lie algebras the commutator is the Lie bracket [x,y] = xy - yx.