#### John Baez

#### Centre for Quantum Technology, September 14, 2018

#### DAMTP, University of Cambridge, October 4, 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.

© 2018 John Baez

baez@math.removethis.ucr.andthis.edu