Lie Group
- Modern Physics -
Quantum Mechanics Dictionary
Definition
A symmetry concept defining transformations that leave key properties of a quantum system invariant. It governs conserved quantities, degeneracies, and selection rules through the action of generators and representations. It does not imply exact invariance when symmetry-breaking terms or boundary effects are present in the Hamiltonian.
Lie Group
- Pure Mathematics -
Algebra Dictionary
Definition
A group that is also a finite-dimensional smooth manifold in which the group operations (multiplication and inversion) are smooth maps; thus it combines algebraic group structure with differential-geometric structure.