Noether's Theorem is perhaps the most beautiful mathematical theorem in physics •It states that: Every continuous symmetry (T) of the Lagrangian has a corresponding conservation lawpic.twitter.com/RrsS1QKm4A
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Caveat (2) Since surface terms do not affect the Euler Lagrange equations, the equations of motion are always trivially invariant upon adding a 4-divergence to the Lagrangian density
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In Quantum Field Theories, however, Noether's theorem can be violated due to quantum effects! A symmetry at the classical level that is broken by quantum corrections is referred to as 'Anomalous' Anomalous symmetries are one of the many great predictions of the Standard Model!pic.twitter.com/Xku5q3MERl
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The reason for this is because Noether's theorem relies on the Euler-Lagrange equations, which need not be satisfied at the quantum level!
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If Noether’s theorem gets 1k likes I will lose my marbles (in a good way)
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I’ve always thought the Lagrangian is really cool, almost too simple
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