This book is printed on acid-free paper.Printed in Singapore by Uto-Print Advanced Electromagnetism and Vacuum Physics Downloaded from www.worldscientific.com by 18.236.198.91 on 05/10/18. For personal use only. V PREFACEThe electromagnetic theory is the most important theory in physics, first because the electromagnetic force is the only force that can be easily manipulated by man with wellknown applications, secondly an extension of this theory in the future may explain all the fundamental forces known to day in nature.A large volume of literature has appeared since the latter days of World war II, written by researchers expanding the basic principles of electromagnetic theory and applying Maxwell's equations to many important practical problems. However, it is my opinion that the electromagnetic theory is not complete and fully understood. A simple example proven these claims is given in this book when the Helmholtz theorem is analyzed. We proved from a mathematical point of view that Maxwell's equations are not complete since a scalar polarization must be taken into account in the equations.It is worth insisting that Maxwell, when he formulated out his theory, was mainly guided by the experimental work performed by the physicists of his time. He tried to give an hydrodynamics understanding of his theory, which is still favored by certain physicists. Even today, Maxwell's equations are given as granted, their validity being justified by experiments. Actually, there is no demonstration of Maxwell's equations from first principles since the mechanical approach used by Maxwell was rapidly abandoned in favor of a novel nonmechanical entity: the electromagnetic field. While the Maxwell's equations can obviously be obtained from a variational principle where they are derived from an action appropriately chosen in order to recover them. In spite of the success of the Maxwell theory in our present technology, we believe that the last word on Maxwell's equations has not been said yet. The reason is that Maxwell's equations raise a number of fundamental questions which have not been answered in a satisfactory manner to date: -One of these questions deals with the existence of a medium sustaining transverse electromagnetic waves.-Another question concerns the fact that Maxwell's equations are not Galilean invariant.-The question of covariance is also strongly related to the electromagnetic induction phenomena, which is difficult to understand within the framework of the special relativity theory.-The discrete nature of the electric charge, where no physical concept has been proposed to explain its quantization, remains one of the deepest mysteries of physics.-There is also the reason why the Lorentz force does not come from the Maxwell's equations, but is additional to them. The reader is reminded that classical electrodynamics demands a connection between the Maxwell's equations and the Lorentz force.In view of a prevalent trend towards a hydrodynamic description of matter and radiation, we propose in this book another...

The authors review the concept of inhomogeneous waves and complete the work done by previous authors. By considering the propagation of an inhomogeneous wave they were able to derive a system of equations which couple Maxwell and potential equations in two different manners and show the importance of the telegrapher's equation with Heaviside's condition.

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