Rotation and Spin in Physics

We delineate the role of rotation and spin in physics, discussing in order Newtonian classical physics, special relativity, quantum mechanics, quantum electrodynamics and general relativity. In the latter case, we discuss the generalization of the Kepler formula to post-Newtonian order $(c^{-2}$) including spin effects and two-body effects. Experiments which verify the theoretical results for general relativistic spin-orbit effects are discussed as well as efforts being made to verify the spin-spin effects

Center of mass, spin supplementary conditions, and the momentum of spinning particles

We discuss the problem of defining the center of mass in general relativity and the so-called spin supplementary condition. The different spin conditions in the literature, their physical significance, and the momentum-velocity relation for each of them are analyzed in depth. The reason for the non-parallelism between the velocity and the momentum, and the concept of "hidden momentum", are dissected. It is argued that the different solutions allowed by the different spin conditions are equally valid descriptions for the motion of a given test body, and their equivalence is shown to dipole order in curved spacetime. These different descriptions are compared in simple examples.Comment: 45 pages, 7 figures. Some minor improvements, typos fixed, signs in some expressions corrected. Matches the published version. Published as part of the book "Equations of Motion in Relativistic Gravity", D. Puetzfeld et al. (eds.), Fundamental Theories of Physics 179, Springer, 201

Field Theory of the Spinning Electron: II — The New Non-Linear Field Equations

One of the most satisfactory picture of spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic electron, that relates the electron spin to the so-called zitterbewegung(zbw). The BZ motion equations constituted the starting point for two recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. Here, employing on the contrary the tensorial language, more common in the (first quantization) field theories, we “quantize” the BZ theory and derive for the electron field a non-linear Dirac equation (NDE), of which the ordinary Dirac equation represents a particular case. We then find out the general solution of the NDE. Our NDE does imply a new probability current J μ , that is shown to be a conserved quantity, endowed (in the center-of-mass frame) with the zbw frequency ω = 2m, where m is the electron mass. Because of the conservation of Jμ , we are able to adopt the ordinary probabilistic interpretation for the fields entering the NDE. At last we propose a natural generalization of our approach, for the case in which an external electromagnetic potential A μ is present; it happens to be based on a new system of five first-order differential field equations