Angular Momentum and Conservation Laws in Classical Electrodynamics

In analogy with mechanics the concepts of field momentum and field angular momentum can be introduced in electrodynamics through conservation laws. In this thesis some fundamental properties of the electromagnetic field angular momentum are treated. This includes the connection to sources, conservation laws and the separation of total angular momentum into a spin and an orbital part. In 1957 Zeldovich pointed out that particles with spin 1/2 must possess, in addition to a magnetic moment, another dipole characteristic. He called it the anapole. Zeldovich's idea was theoretically clarified and generalized in the 1970's and an entire class of moments were introduced. These were called the toroidal multipoles and they constitute a family of multipoles independent of electric and magnetic moments. Their relation to the electromagnetic angular momentum is discussed, however, as the standard procedure found in most textbooks implicitly contains these multipoles, their introduction do not seem to yield fundamentally new results. The fields, intensity and angular momentum from a toroidal dipole is given in this thesis. A new expression for electromagnetic angular momentum in terms of retarded integrals of the sources is given, and the angular momentum density from an electric dipole is calculated using this expression. Research on the photon orbital angular momentum is a hot topic today with applications in various fields. Recent publications suggest the possibility to use the orbital angular momentum of the electromagnetic fields in radio. Conservation laws for fields in an orbital angular momentum eigenstate are derived, where analogies with the linear momentum and stress tensor, in terms of the eigenmodes, are introduced. A separation of angular momentum into its spin and orbital parts would have a major impact on the applications of orbital angular momentum since then the orbital structure of the field could be measured directly. A complex Lagrangian density is constructed from the complex field strength tensor and its dual tensor. The corresponding field equations are Maxwell's equations in Majorana form, expressed in Riemann-Silberstein vectors. The conservation laws due to translational, Lorentz, and phase transformations are derived using Noether's theorem. The symmetry of translational invariance yields the Maxwell stress tensor. However, within the expression provided by Noether's theorem, another rank two tensor, which describes the (wave) polarization of the electromagnetic fields, also appears but ultimately cancels. The conservation law can be interpreted as the sum of two separate conservation laws, one for right-handed and one for left-handed fields, which appear …