The topics in this volume range from mathematical aspects of the theory of the Poincar‚ group, Clifford algebras and the CPT theorem, through new theoretical physical constructions and concepts (such as the physical significance of the 4-potential, the interplay between quantum mechanics and gravity, Majorana-like models, the photon as a composite particle, action-at-a-distance and superluminal phenomena), to experiments in neutrino physics. The book will be of interest to graduate students and researchers working in fundamental physics and phenomenology, and also to experimentalists.

This book is about Maxwell's electromagnetic theory of light. First, it is a fully relativistic theory without having a non-relativistic limit. There arise many difficulties in quantising the electromagnetic field and in the physical interpretation of the wavefunction of its quanta. Further, the first quantisation of the Maxwell equations similar to quantisation of classical mechanics by the Schrodinger method, has not been discussed in most books on quantum mechanics. Second, the Maxwell field is the simplest gauge field possessing symmetry with respect to Poincare group of transformations in addition to scale, duality and special conformal transformations whose local versions give rise to new interaction of photons through new gauge fields. One of these gauge fields couples to the spin density of the photon and other particles and can bind fermion-antifermion pairs to give transverse photons. Another interesting aspect of the electromagnetic field is its coherence properties and their interpretation in terms of quantised theory.

th The 29 International Conference was held as the first one of the millennium at its Fort Lauderdale venue. These conferences began, with High Energy Physics being the main topic, by introducing gradually cosmology into its programs. These proceedings of the 2000 conference reflect the variety of topics and ideas discussed. Our future conferences will be designed somewhat akin to the early Coral Gables Conferences where we shall seek some convergence of ideas. For this reason various committees have been formed from among the participating physicists. The committees and their memberships are listed in these proceedings. We further decided for the first time to include some graduate student participants in our future meetings for which also a committee has already been established. The topics will demonstrate a more activist structure of the Coral Gables Conferences, for example the duality of the gravitational forces and expansion of the universe will be discussed from this point of view since it conveys a convergence to the ideas of quintessence versus the ordinary theory, which are considered as the cause of the expansion of the universe. We further wish to announce that the future conferences will assume a collective organization where several committees as listed in these proceedings will have their input into the conference. We have now introduced new topics and ideas, which referred especially to the attractive and repulsive nature of the gravitational force. These proceedings of the conference contain a variety of topics and ideas.

This book lays the foundations of the theory of fluctuating multivalued fields with numerous applications. Most prominent among these are phenomena dominated by the statistical mechanics of line-like objects, such as the phase transitions in superfluids and superconductors as well as the melting process of crystals, and the electromagnetic potential as a multivalued field that can produce a condensate of magnetic monopoles. In addition, multivalued mappings play a crucial role in deriving the physical laws of matter coupled to gauge fields and gravity with torsion from the laws of free matter. Through careful analysis of each of these applications, the book thus provides students and researchers with supplementary reading material for graduate courses on phase transitions, quantum field theory, gravitational physics, and differential geometry.

This book contains the Proceedings of the Fifth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington from June 28 to July 2, 2010. The Meeting focused on tests of these fundamental symmetries and on related theoretical issues, including scenarios for possible violations. Topics covered at the meeting include searches for CPT and Lorentz violations involving: birefringence and dispersion from cosmological sources, clock-comparison measurements, CMB polarization, electromagnetic resonant cavities, equivalence principle, gauge and Higgs particles, high-energy astrophysical observations, laboratory and gravimetric tests of gravity, matter interferometry, neutrino oscillations, oscillations and decays of K, D, B mesons, particle-antiparticle comparisons, post-newtonian gravity in the solar system and beyond, second- and third-generation particles, space-based missions, spectroscopy of hydrogen and antihydrogen, and spin polarized matter. Theoretical discussions include physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; and related classical and quantum issues in field theory, particle physics, gravity, and string theory.

This book deals with fields which possess different spins so, that there is an additional internal symmetry of such schemes. The main feature of theories with multi-spin is that transformations of the Lorentz and internal symmetry groups do not commute each other. So, parameters of the group are tensors but not scalars as in the more common-gauge theories. This kind of symmetry is also different from supersymmetry where group parameters are not scalars. The difference is that in this case the algebra of generators of the symmetry is closed without adding the generators of the Poincaré group. Consideration of schemes of fields with multi-spin possess some attractive features and avoid some difficulties but the price of this is the presence of the indefinite metric. It should be noted that some quantum theories of gravity also require the introduction of an indefinite metric. The localisation of parameters of the internal symmetry group leads to the gauge fields and field interactions. In Part II solutions are found for equations for particles with different spins in external classical and quantified electromagnetic fields, as well as the interaction of fields with multi-spin with external electromagnetic fields of different configurations.

The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.

The Marcel Grossmann meetings were conceived to promote theoretical understanding in the fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. They review recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main objective is to bring together scientists from diverse backgrounds and their range of topics is broad, from more abstract classical theory and quantum gravity and strings to more concrete relativistic astrophysics observations and modeling.This Tenth Marcel Grossmann Meeting was organized by an international committee composed of D Blair, Y Choquet-Bruhat, D Christodoulou, T Damour, J Ehlers, F Everitt, Fang Li Zhi, S Hawking, Y Ne'eman, R Ruffini (chair), H Sato, R Sunyaev, and S Weinberg and backed by an international coordinating committee of about 135 members from scientific institutions representing 54 countries. The scientific program included 29 morning plenary talks during 6 days, and 57 parallel sessions over five afternoons, during which roughly 500 papers were presented.These three volumes of the proceedings of MG10 give a broad view of all aspects of gravitation, from mathematical issues to recent observations and experiments.

The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

Jean-Pierre Vigier continually labeled one of les heretiques de la science, l’eternel resistant et le patriarche is yet a pillar of modern physics and mathematics, with one leg firmly planted in theory and the other in empiricism spanning a career of nearly 60 years with a publication vitae quickly approaching 400! He wrote of his mentor Louis de Broglie “Great physicists fight great battles”, which perhaps applies even more so to 1 Jean-Pierre Vigier himself . If fortune allows a visit to Paris, reported to be the city of love, and certainly one of the most beautiful and interesting cities in the world; one has been treated to a visual and cultural feast. For example a leisurely stroll from the Musee du Louvre along the Champs-Elysees to the Arc de Triomphe would instill even the least creative soul with the entelechies of a poets muse. It is perhaps open to theoretical interpretation, but if causal conditions have allowed one to be a physicist, visiting Paris, one may have taken opportunity to visit the portion of the old Latin quarter in place Jussieu where Pierre et Marie Curie Universite, reported to be ‘the best university in France’, is stationed.