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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Quantum Field Theory II

MP 11.3: Talk

Thursday, April 3, 2025, 16:55–17:15, ZHG001

Gauge invariance of topological charges of Noether current — •Christian Hembd — Montebellunastrasse 5, 73447 Oberkochen

Free (complex) quantum fields have an associated Noether current due to global phase invariance of their Lagrangian. By help of the degree of a mapping and the index of a zero known from algebraic topology it is possible to define Lorentz invariant topological charges of the Noether current. These charges are invariant under a group of local transformations of the quantum field. For the case of a free fermion field this leads to SU(2) gauge invariance.

Keywords: gauge invariance; topological charge; Noether current; mapping degree