Theoretical Physics

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way.

This concise treatment embraces, in four parts, all the main aspects of theoretical physics. Recent topics such as holography and quantum cryptography are included. The book summarizes what a graduate student, physicist working in industry, or a physics teacher should master during his or her degree course. It will also be useful for deepening one’s insight and it adds new dimensions to understanding of these elemental concepts.

Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as “decoherence”.

HISTORICAL PRELUDE Ettore Majorana's fame solidly rests on testimonies like the following, from the evocative pen of Giuseppe Cocconi. At the request of Edoardo Amaldi, he wrote from CERN (July 18, 1965): "In January 1938, after having just graduated, I was invited, essen­ tially by you, to come to the Institute of Physics at the University in Rome for six months as a teaching assistant, and once I was there I would have the good fortune of joining Fermi, Bernardini (who had been given a chair at Camerino a few months earlier) and Ageno (he, too, a new graduate), in the research of the products of disintegration of /-L "mesons" (at that time called mesotrons or yukons), which are produced by cosmic rays [ . . . ] "It was actually while I was staying with Fermi in the small laboratory on the second floor, absorbed in our work, with Fermi working with a piece of Wilson's chamber (which would help to reveal mesons at the end of their range) on a lathe and me constructing a jalopy for the illumination of the chamber, using the flash produced by the explosion of an aluminum ribbon short circuited on a battery, that Ettore Majorana came in search of Fermi. I was introduced to him and we exchanged few words. A dark face. And that was it.

Einstein's theory of gravitation is perhaps one of the best-established theories ever conceived. However, it is based on the hypothesis that space-time carries curvature alone, leaving torsion out. Because torsion is a natural part of the most general geometric background in which Einstein gravity is built, it is all too natural that the torsional completion of gravity should be considered. Constructing an underlying stage in which both curvature and torsion are present, the fact that curvature couples with energy suggests that torsion may couple with spin, which is the other conserved quantity in quantum field theory. Torsion-gravity with spinning matter is, therefore, a complete and self-consistent setting for modern physics, with potential applications wherever spin effects may be important, stretching from quantum mechanics to the standard models of particle physics and early cosmology. However, this fact is not as present in today's literature as it might be. The scope of the present collection of papers is to consolidate the wisdom of various experts in the field so as to clarify the present status of torsion in gravity and spin in quantum field theory.

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area,

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals.

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals.