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What is the physical meaning of a Lie algebra symmetry?

The physical meaning of a Lie group symmetry is clear: for example, if you have a quantum system whose states have values in some Hilbert space $H$, then a Lie group symmetry of the system means that ...
10
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2answers
2k views

Noether's Theorem in Quantum Mechanics

In classical mechanics: If a Lagrangian L is preserved by an infinitesimal change in the state space variables qi -> qi + εKi(q) leads to only second order change in the Lagrangian: $$ 0 = ...