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Gauge invariant Noether’s theorem and the proton spin crisis

  • Gouranga C. Nayak
Open Access
Regular Article - Theoretical Physics
  • 61 Downloads

Abstract

Due to proton spin crisis it is necessary to understand the gauge invariant definition of the spin and orbital angular momentum of the quark and gluon from first principle. In this paper we derive the gauge invariant Noether’s theorem by using combined Lorentz transformation plus local gauge transformation. We find that the notion of the gauge invariant definition of the spin (or orbital) angular momentum of the electromagnetic field does not exist in Dirac-Maxwell theory although the notion of the gauge invariant definition of the spin (or orbital) angular momentum of the electron exists. We find that the gauge invariant definition of the spin angular momentum of the electromagnetic field in the literature is not correct because of the non-vanishing surface term in Dirac-Maxwell theory although the corresponding surface term vanishes for linear momentum. We also show that the Belinfante-Rosenfeld tensor is not required to obtain symmetric and gauge invariant energy-momentum tensor of the electron and the electromagnetic field in Dirac-Maxwell theory.

Keywords

Gauge Symmetry Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.C.N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookU.S.A.

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