Representation theory of the Galilean group information
Representation theory of the symmetries of non-relativistic quantum space
Lie groups and Lie algebras
Classical groups
General linear GL(n)
Special linear SL(n)
Orthogonal O(n)
Special orthogonal SO(n)
Unitary U(n)
Special unitary SU(n)
Symplectic Sp(n)
Simple Lie groups
Classical
An
Bn
Cn
Dn
Exceptional
G2
F4
E6
E7
E8
Other Lie groups
Circle
Lorentz
Poincaré
Conformal group
Diffeomorphism
Loop
Euclidean
Lie algebras
Lie group–Lie algebra correspondence
Exponential map
Adjoint representation
Killing form
Index
Simple Lie algebra
Loop algebra
Affine Lie algebra
Semisimple Lie algebra
Dynkin diagrams
Cartan subalgebra
Root system
Weyl group
Real form
Complexification
Split Lie algebra
Compact Lie algebra
Representation theory
Lie group representation
Lie algebra representation
Representation theory of semisimple Lie algebras
Representations of classical Lie groups
Theorem of the highest weight
Borel–Weil–Bott theorem
Lie groups in physics
Particle physics and representation theory
Lorentz group representations
Poincaré group representations
Galilean group representations
Scientists
Sophus Lie
Henri Poincaré
Wilhelm Killing
Élie Cartan
Hermann Weyl
Claude Chevalley
Harish-Chandra
Armand Borel
Glossary
Table of Lie groups
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In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the Galilean group, which is the spacetime symmetry group of nonrelativistic quantum mechanics.
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