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| ⚫ | In ] and ], in addition to the ] ] symmetry related to the ], there are also position dependent ]s. ] states that for every infinitesimal symmetry transformation that is local (local in the sense that the transformed value of a field at a given point only depends on the field configuration in an arbitrarily small neighborhood of that point), there is a corresponding conserved charge called the ], which is the space integral of a Noether density (assuming the integral converges and there is a ] satisfying the ]). | ||
| ⚫ | An '''infraparticle''' is an electron. In ] and ], in addition to the ] ] symmetry related to the ], there are also position dependent ]s. ] states that for every infinitesimal symmetry transformation that is local (local in the sense that the transformed value of a field at a given point only depends on the field configuration in an arbitrarily small neighborhood of that point), there is a corresponding conserved charge called the ], which is the space integral of a Noether density (assuming the integral converges and there is a ] satisfying the ]). | ||
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An infraparticle is an electron. In electrodynamics and quantum electrodynamics, in addition to the global U(1) symmetry related to the electric charge, there are also position dependent gauge transformations. Noether's theorem states that for every infinitesimal symmetry transformation that is local (local in the sense that the transformed value of a field at a given point only depends on the field configuration in an arbitrarily small neighborhood of that point), there is a corresponding conserved charge called the Noether charge, which is the space integral of a Noether density (assuming the integral converges and there is a Noether current satisfying the continuity equation).
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