In this talk I will present how symmetries are treated in a recent C*-algebraic formulation of interacting quantum field theory provided in [2108.13336]. One of the main results of that work was non-perturbative formulation of what we called “anomalous quantum Noether theorem.” It can be seen as the natural counterpart of the classical Noether theorem, which works in quantum theory also in the presence of anomalies.
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