John Baez

Centre for Quantum Technology, September 14, 2018

DAMTP, University of Cambridge, October 4, 2018

Philosophy and Physics of Noether's Theorems: A Centenary Conference on the 1918 Work of Emmy Noether, October 7, 2018

Getting to the Bottom of Noether's Theorem

In her paper of 1918, Noether's theorem relating symmetries and conserved quantities was formulated in term of Lagrangian mechanics. But if we want to make the essence of this relation seem as self-evident as possible, we can turn to a formulation in term of Poisson brackets, which generalizes easily to quantum mechanics using commutators. This approach also gives a version of Noether's theorem for Markov processes. The key question then becomes: when, and why, do observables generate one-parameter groups of transformations? This question sheds light on why complex numbers show up in quantum mechanics.

You can see the slides here, and also the paper I wrote:

• John Baez, Getting to the bottom of Noether's theorem, in The Philosophy and Physics of Noether's Theorems: A Centenary Conference, eds. Bryan W. Roberts and Nicholas Teh, Cambridge U. Press, Cambridge, 2022.

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