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Register a new userOn the radiation of an arbitrary moving constant magnetic moment
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It is demonstrated that a constant magnetic moment does not emit electo-magnetic radiation while moving in an arbitrary field
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It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz transformations. The electrodynamics problem can then be treated within a single inertial frame description. To evaluate radiation fields from moving charged particles we need their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newtons second law corrected for the relativistic dependence of the particle momentum on the velocity. In all standard derivations the trajectories in the source part of the usual Maxwells equations are identified with the trajectories $vec{x}(t)$ calculated by using the corrected Newtons second law. This way of coupling fields and particles is considered correct. We argue that this procedure needs to be changed by demonstrating a counterintuitive: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. The trajectory of a particle in the lab frame consistent with the usual Maxwells equations, is found by solving the dynamics equation in manifestly covariant form, with the proper time $tau$ used to parameterize the particle world-line in space-time. We find a difference between the true particle trajectory $vec{x}(t)$ calculated or measured in the conventional way, and the covariant particle trajectory $vec{x}_{cov}(t)$ calculated by projecting the world-line to the lab frame and using t to parameterize the trajectory curve. The difference is due to a choice of convention, but only $vec{x}_{cov}(t)$ is consistent with the usual Maxwells equations: therefore, a correction of the conventional synchrotron-cyclotron radiation theory is required.
The Goldberger-Treiman relation $M=2pi/sqrt{3}f^{rm cl}_pi$ where $M$ is the constituent quark mass in the chiral limit (cl) and $f^{rm cl}_pi$ the pion decay constant in the chiral limit predicts constituent quark masses of $m_u=328.8pm 1.1$ MeV and $m_d=332.3pm 1.1$ MeV for the up and down quark, respectively, when $f^{rm cl}_pi=89.8pm 0.3$ MeV is adopted. Treating the constituent quarks as bare Dirac particles the following zero order values $mu^{(0)}}_p=2.850pm 0.009$ and $mu^{(0)}}_n= -1.889pm 0.006$ are obtained for the proton and neutron magnetic moments, leading to deviations from the experimental data of 2.0% and 1.3%, respectively. These unavoidable deviations are discussed in terms of contributions to the magnetic moments proposed in previous work.
A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude.
The action functional for a linear elastic medium with dislocations is given. The equations of motion following from this action reproduce the Peach-K{o}hler and Lorentzian forces experienced by dislocations. The explicit expressions for singular and finite parts of the self-force acting on a curved dislocation are derived in the framework of linear theory of elasticity of an isotropic medium. The velocity of dislocation is assumed to be arbitrary but less than the shear wave velocity. The nonrelativistic and ultrarelativistic limits are investigated. In the ultrarelativistic limit, the explicit expression for the leading contribution to the self-force is obtained. In the case of slowly moving dislocations, the effective equations of motion derived in the present paper reproduce the known results.
We investigate the radiation from a charged particle moving outside a dielectric cylinder parallel to its axis. It is assumed that the cylinder is immersed into a homogeneous medium. The expressions are given for the vector potential and for the electric and magnetic fields. The spectral distributions are studied for three types of the radiations: (i) Cherenkov radiation (CR) in the exterior medium, (ii) radiation on the guided modes of the dielectric cylinder, and (iii) emission of surface polaritons. Unlike the first two types of radiations, there is no velocity threshold for the generation of surface polaritons. The corresponding radiation is present in the spectral range where the dielectric permittivities of the cylinder and surrounding medium have opposite signs. The spectral range of the emitted surface polaritons becomes narrower with decreasing energy of the particle. The general results are illustrated for a special case of the Drude model for dispersion of the dielectric permittivity of the cylinder. We show that the presence of the cylinder may lead to the appearance of strong narrow peaks in the spectral distribution of the CR in the exterior medium. The conditions are specified for the appearance of those peaks and the corresponding heights and widths are analytically estimated. The collective effects of particles in bunches are discussed.
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