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Discusses the concepts and mathematics behind the author's research works on the foam model, as applied to studying issues of phase stability and elasticity for various non-closed packed structures found in fuzzy and colloidal crystals, as well as on a renormalization-group analysis regarding the critical behavior of loop polymers.

These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course on Quantum Field Theory.

The aim of the book is to give an introduction to the method of QCD Spectral Sum Rules and to review its developments. After some general introductory remarks, Chiral Symmetry, the Historical Developments of the Sum Rules and the necessary materials for perturbative QCD including the MS regularization and renormalization schemes are discussed. The book also gives a critical review and some improvements of the wide uses of the QSSR in Hadron Physics and QSSR beyond the Standard Hadron Phenomenology. The author has participated actively in this field since 1978 just before the expanding success of the SVZ QSSR.

In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues: It only presupposes standard calculus. It allows to justify manipulations necessary in physical applications.The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.

Starting from Boltzmann's formula, this text formulates the microcanonical thermodynamics entirely within the frame of mechanics. Attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.

This book explains the physics and phenomenology of massive neutrinos. The authors argue that neutrino mass is not unlikely and consider briefly the search for evidence of this mass in decay processes before they examine the physics and phenomenology of neutrino oscillation. The physics of Majorana neutrinos (neutrinos which are their own antiparticles) is then discussed. This volume requires of the reader only a knowledge of quantum mechanics and of very elementary quantum field theory.

These lecture notes provide a course on modern, co-ordinate-free differential geometry. They introduce general topology and co-ordinate-free differential geometry, examine geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and cover the theory of fibre bundles.

Volume 58 in the WORLD SCIENTIFIC LECTURE NOTES IN PHYSICS series.This volume constitutes a course on a number of central concepts of solid state physics, such as the classification of solids, band theory, the developments in one-electron band theory with the presence of perturbation, effective Hamilton theory, and other theories.

Supersymmetry is a symmetry which combines bosons and fermions in the same multiplet of a larger group which unites the transformations of this symmetry with that of spacetime. This title provides an introduction to supersymmetry, and begins with a chapter on spacetime symmetries and spinors. It also addresses the breaking of supersymmetry.

Begins by introducing the effective field approach, the simplest approach to phase transitions. This book provides an intuitive approximation to the physics of diverse phenomena such as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity.

Provides an introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD. This title also provides the reader with the necessary analytical and numerical techniques to carry out research on his own. It introduces the reader to problems which are under intensive investigation.

An introduction to various issues related to the theory and phenomenology of massive neutrinos for the nonexpert, also providing a discussion of results in the field for the active researcher. All the necessary techniques and logics are included and topics such as supersymmetry are covered.

This work is an extensive set of lecture notes on various aspects of non-perturbative quantum chromodynamics - the fundamental theory of strong interaction on which nuclear and hadronic physics is based.

Develops the techniques of perturbative QCD in pedagogical detail starting with field theory. Providing a comprehensive introduction to gauge theories, this book offers extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions.

Describes quantum field theory within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas. This book also covers path integral quantization of gauge theories and anomalies, and more.