Applications to Physics and Vice Versa
Lie groups and their algebras arise most often in physics as symmetry groups of dynamical systems. These symmetries are intimately associated with conservation laws. For example, if a physical system is invariant under translations then its linear momentum is conserved; while rotational invariance of a system implies conservation of angular momentum. In modern physics the symmetry groups are not only the geometrical symmetries of space-time, but also new symmetries associated with “internal” degrees of freedom of particles and fields. These symmetries lead to the conservation of more exotic quantities such as isospin, strangeness, charm, etc.
KeywordsAngular Momentum Harmonic Oscillator Commutation Relation Poisson Bracket Canonical Variable
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