CLASSICAL ELECTRODYNAMICS

The teaching of classical electrodynamics has as its first goal the deepening of the study of electromagnetism from relativistic point of view. Are introduced the elements of the calculus of variations that lead to the Lagrangian and Hamiltonian formalism in the study of the interaction of a charge with an electromagnetic field. The formalism of Lagrangian mechanics is then used for the purpose of Lagrangian and Hamiltonian formulation of Maxwell's equations. The latter approach allows to study any deviations from ordinary Maxwell's theory as the effects of photon mass within the theory of Maxwell-Proca. The second part of the programme covers or study of the classical theory of radiation, the method of Hertz potentials and the so called radiation reaction. In the third part, some aspects of electrodynamics of plasmas are discussed and in particular those relating to fusion plasmas to share interest in future energy production. Finally, the fourth part deals with some of the topics related to the foundations of special relativity and the formulation of the so-called "extended relativity".

1) Covariant formulation of electromagnetism

Summaries of Maxwell equations - Helmoltz decomposition theorem - Basic equations of geometric optics - Eikonal equation and its geometric interpretation - Differential rays equation: general and stratified medium cases - Potentials of electromagnetic field and gauge invariance - Green function method for the wave equation solution - Maxwell equations in covariant four-vector Minkowski-force-density form of force and energy-momentum tensor of c.e.m.-elements of calculus of variations - Remarkable l emmas of the calculus of variations - Special cases of the Euler-Lagrange equation: brachistochrone and mirages - Relativistic formulation of Lagrangian mechanics – Lagrangian and Hamiltonian of a charged in an electromagnetic external field - Relativistic angular momentum - Relativistic motion of charges in uniform electric and magnetic fields – Inelastic processes thresholds – Non additivity of proper mass - Lagrangian Formulation for continuous systems and fields-Lagrangian of the electromagnetic field – Conservation theorems : energy-momentum tensor canonical – Energy-momentum tensor symmetrization: Belifante procedure – Electromagnetic field Hamiltonian - Maxwell-Proca Equations and generalization of Poynting theorem – Some theoretical consequences resulting from the assumption of photons with nonzero mass: magnetostatic and electrostatic effects, scattering of plane waves in a vacuum – Typical experiments to predict the upper limit for the photon mass.

2) Classical theory of radiation

Electromagnetic field in the wave zone - Fourth-moment emission - Radiation spectrum emitted by accelerated charge - Hertz potential vectors - Irradiation from an oscillating electric and magnetic dipole - Force law between two in motion charged electric charges - Compton backward diffusion - Reaction of radiation - Heuristic derivation of the Abraham-Lorentz equation - Electromagnetic mass: qualitative considerations - Direct calculation of the reaction of the radiation from the delayed fields - Properties of the motion equations of a charge subjected to external forces and to the self-force.

3) Plasma Physics Electrodynamics elements (*)

Phase space and distribution function – Liouville's theorem - Boltzmann and Vlasov equations - Plasma in an electromagnetic field - Magnetohydrodynamic (MHD) Equations – Equations for a fluid MHD model and static solutions - Squeezing effect – Cyclotron radiation – Fusion Plasmas - Forcefully and thermonuclear ignition: ignition temperature and Lawson criterion – Controlled thermonuclear fusion : magnetic confinement and inertial confinement – The Tokamak.

4) Fundamentals of the special extended relativity theory (*)
Conventionality of the synchronization method: topological and metric simultaneity - Reichenbach synchronization (nonstandard) - One-dimensional synchrony trasformation - Dependence on the direction of the synchronization parameter - Three-dimensional synchrony transformation and its properties - An alternative formulation of extended relativity: general transformations for the space-time coordinates - One-way speed of light - The Lorentz transformations as a special case of the general transformations - Role of two postulates of Einstein in the determination of the parameters - Speed round-trip light - Weak relativity and equivalent transformations - Synchronization methods: of symmetric speeds, slow transport and absolute - Mathematical properties of equivalent transformations - Conventional aspects of the special theory of relativity and purely relativistic phenomena - Experimental tests of extended relativity.

(*) Depending on the time available these chapters could also be carried out alternatively.

V. Barone : Relatività - Bollati Boringhieri

H. Goldstein : Meccanica classica - Zanichelli

L. Lovitch, S. Rosati : Fisica Generale: Elettricità,Magnetismo, Elettromagnetismo,

Relatività ristretta, Ottica, Meccanica quantistica - C.E.A.

J.D. Jackson : Elettrodinamica classica - Zanichelli

L. Landau : Teoria classica dei campi - Ed. Riuniti

L. Landau : Elettrodinamica dei mezzi continui - Ed. Riuniti

G. Pucella, S.E. Segrè : Fisica dei Plasmi, Zanichelli

J. M. Rax : Physique des Plasmas, Dunod, Paris

H. Reichenbach : Axiomatization of the theory of relativity, University of

California Press 1969

H. Reichenbach : The philosophy of space and time, Dover publications, Inc.

The student is free to choose any other text at the university level.