3. (a) The electric charge is conserved in electrodynamics. This conservation law is related to gauge...
3. (a) The electric charge is conserved in electrodynamics. This conservation law is related to gauge symmetry. What is the gauge group? (b) The gauge covariant derivative in electrodynamics is given by D = 2, - iA. - (2) What is the generator of the gauge group? (c) What is the gauge curvature F v in electrodynamics? (Hint: The gauge curvature F is related to D. by the relation (DxD] = ief. This is similar to GR or Riemannian geometry, in which the space-time curvature is defined through the commutator of the usual covariant derivative d in Riemannian geometry), i.e., d., V =R..V.) (d) F is a symmetric tensor of the second rank. (True or False) (e) Is there any relation between F. and Maxwell's equations? (Hint: Find an identity relation of F first.)