Covariance And Gauge Invariance In Continuum Physics

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

This book provides a thorough description of the manifestly covariant canonical formalism of the abelian and non-abelian gauge theories and quantum gravity. The emphasis is on its non-perturbative nature and the non-use of the path-integral approach. The formalism presented here is extremely beautiful and transparent.

In August/September 2000, a group of 80 physicists from 53 laboratories in 15 countries met in Erice, Italy, to participate in the 38th Course of the International School of Subnuclear Physics. This book constitutes the proceedings of that meeting. It focuses on the theoretical investigation of several basic unity issues, including: (1) the understanding of gauge theories in both their continuum and lattice versions; (2) the possible existence and relevance of large extra dimensions together with the resultant lowering of the Planck/string scale to the TeV range; (3) the origin and structure of flavour mixing in the quark and lepton (neutrino) sectors.

The sixth Ettore Majorana International School of Mathematical Physics was held at the Centro della Cultura Scientifica Erice, Sicily, 1-14 July 1985. The present volume collects lecture notes on the ses sion which was devoted to Fundamental Problems of Gauge Field Theory. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now pro vides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lectures and seminars of the school concentrated on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, we mention the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the explora tion of the extraordinary enigmatic connections between Kac-Moody Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories.

Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. This book provides precise presentations of exact continuum theories on materially non-uniform or non-simple bodies that can respond to short- and long-range inter-particle loads and fields. This volume consists of three parts. Part I is devoted to the study of continuum field theories for bodies having inner structure. All materials, to some extent, are composed of particles that behave like small rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. The developments of nonlocal theories of nonpolar and polar continua are covered in Parts II and III. This publication is valuable to students and researchers interested in polar and nonlocal field theories.

This book introduces the reader to an area of elementary particle physics which has been the subject of intensive research in the past two decades. It provides graduate students with the basic theoretical background on quantum gauge field theories formulated on a space-time lattice, and with the computational tools for carrying out research in this field. The book is a substantially extended version of the first edition which appeared in 1992. Much effort has been invested to present the material in a transparent way, and in exemplifying subtle points in simple models. The material covered should enable the reader to follow the vast literature on the subject without too much difficulties. Hopefully the book will motivate young physicists to carry out research in this area of elementary particle physics. Request Inspection Copy