Rabounski D. Fields, Vacuum and the Mirror Universe 2009

Textbook in PDF format

The cornerstone of this book is that when tackling the problems of the General Theory of Relativity we had to amend the existing theory with some new mathematical techniques. In their famous The Classical Theory of Fields, which has already become a de facto standard for a university reference book on the General Theory of Relativity, Lev Landau and Evgeny Lifshitz give an excellent account of the theory of motion of particles in gravitational and electromagnetic fields. They however, employed only the usual generally covariant method of analysis. The mathematical method of chronometric invariants (physically observable quantities in the General Theory of Relativity) had not yet been developed at that time (the middle of the 1930’s). We now feel that this method should also be taken into account. Therefore, in the process of writing this book, we have had to face the necessity to introduce the mathematical method of chronometric invariants into the existing theory of motion of particles in gravitational and electromagnetic fields. Moreover, the motion of spin-particles was not covered by Landau and Lifshitz. Therefore, in our book, a separate consideration has been given to the motion of particles with inner rotational momentum (spin). We have also added a chapter with an account of tensor algebra and analysis in terms of chronometric invariants. All these make our book a contemporary supplement to The Classical Theory of Fields