Heisenberg group

The Heisenberg group is a mathematical structure that arises in the study of quantum mechanics and geometry. It captures the idea that certain pairs of properties, like position and momentum, cannot both be precisely measured at the same time—this is a fundamental concept called the uncertainty principle. Mathematically, the Heisenberg group is a set of points equipped with a special way of combining them (called a “group operation”) that models this non-commutative behavior. It’s essential in understanding how quantum systems behave and also appears in areas like harmonic analysis and geometric group theory.