Surveys the monopole problem on a few different levels, from classical electrodynamics up to N=2 SUSY Yang-Mills theory. and presents a compact, `bird's eye view' on the entire set of problems related with very notion of monopole including actual stand of the problem, related historical remarks and comprehensive bibliography. Presents original results obtained by the author in collaboration with other researches are presented as well as it summarizes the present status of the theory of monopoles and provides an introduction to the field.

In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

For scientific, technological and organizational reasons, the end of World War II (in 1945) saw a rapid acceleration in the tempo of discovery and understanding in nuclear physics, cosmic rays and quantum field theory, which together triggered the birth of modern particle physics. The first fifteen years (1945-60) following the war's end ? the ?Startup Period? in modern particle physics -witnessed a series of major experimental and theoretical developments that began to define the conceptual contours (non-Abelian internal symmetries, Yang-Mills fields, renormalization group, chirality invariance, baryon-lepton symmetry in weak interactions, spontaneous symmetry breaking) of the quantum field theory of three of the basic interactions in nature (electromagnetic, strong and weak). But it took another fifteen years (1960-75) ? the ?Heroic Period? in modern particle physics ? to unravel the physical content and complete the mathematical formulation of the standard gauge theory of the strong and electroweak interactions among the three generations of quarks and leptons. The impressive accomplishments during the ?Heroic Period? were followed by what is called the ?period of consolidation and speculation (1975-1990)?, which includes the experimental consolidation of the standard model (SM) through precision tests, theoretical consolidation of SM through the search for more rigorous mathematical solutions to the Yang-Mills-Higgs equations, and speculative theoretical excursions ?beyond SM?.Within this historical-conceptual framework, the author ? himself a practicing particle theorist for the past fifty years ? attempts to trace the highlights in the conceptual evolution of modern particle physics from its early beginnings until the present time. Apart from the first chapter ? which sketches a broad overview of the entire field ? the remaining nine chapters of the book offer detailed discussions of the major concepts and principles that prevailed and were given wide currency during each of the fifteen-year periods that comprise the history of modern particle physics. Those concepts and principles that contributed only peripherally to the standard model are given less coverage but an attempt is made to inform the reader about such contributions (which may turn out to be significant at a future time) and to suggest references that supply more information. Chapters 2 and 3 of the book cover a range of topics that received dedicated attention during the ?Startup Period? although some of the results were not incorporated into the structure of the standard model. Chapters 4-6 constitute the core of the book and try to recapture much of the conceptual excitement of the ?Heroic Period?, when quantum flavordynamics (QFD) and quantum chromodynamics (QCD) received their definitive formulation. [It should be emphasized that, throughout the book, logical coherence takes precedence over historical chronology (e.g. some of the precision tests of QFD are discussed in Chapter 6)]. Chapter 7 provides a fairly complete discussion of the chiral gauge anomalies in four dimensions with special application to the standard model (although the larger unification models are also considered). The remaining three chapters of the book (Chapters 7-10) cover concepts and principles that originated primarily during the ?Period of Consolidation and Speculation? but, again, this is not a literal statement. Chapters 8 and 9 report on two of the main directions that were pursued to overcome acknowledged deficiencies of the standard model: unification models in Chapter 8 and attempts to account for the existence of precisely three generations of quarks and leptons, primarily by means of preon models, in Chapter 9. The most innovative of the final three chapters of the book is Chapter 10 on topological conservation laws. This last chapter tries to explain the significance of topologically non-trivial solutions in four-dimensional (space-time) particle physics (e.g. 't Hooft-Polyakov monopoles, instantons, sphalerons, global SU(2) anomaly, Wess-Zumino term, etc.) and to reflect on some of the problems that have ensued (e.g. the ?strong CP problem? in QCD) from this effort. It turns out that the more felicitous topological applications of field theory are found ? as of now ? in condensed matter physics; these successful physical applications (to polyacetylene, quantized magnetic flux in type-II low temperature superconductivity, etc.) are discussed in Chapter 10, as a good illustration of the conceptual unity of modern physics.

Yi-Shi Duan (1927-2016) was one of the world-renowned pioneers in the study of gauge field theory and general relativity. Trained in the former Soviet Union, Prof. Duan returned to China in 1957 to work in Lanzhou University for 60 years. In 1963, he came up with a general co-variant form of the conservation law of the energy-momentum tensor in general relativity. In 1979, he suggested that the gauge potential could be decomposed, which has important implications to gauge field theory. He trained in China a big team of talents in theoretical physics. His contributions to theoretical physics in China have earned him praise from both Professor Shiing-Shen Chern and Professor Chen-Ning Yang.

What makes a good experiment? Although experimental evidence plays an essential role in science, as Franklin argues, there is no algorithm or simple set of criteria for ranking or evaluating good experiments, and therefore no definitive answer to the question. Experiments can, in fact, be good in any number of ways: conceptually good, methodologically good, technically good, and pedagogically important. And perfection is not a requirement: even experiments with incorrect results can be good, though they must, he argues, be methodologically good, providing good reasons for belief in their results. Franklin revisits the same important question he posed in his 1981 article in the British Journal for the Philosophy of Science, when it was generally believed that the only significant role of experiment in science was to test theories. But experiments can actually play a lot of different roles in science—they can, for example, investigate a subject for which a theory does not exist, help to articulate an existing theory, call for a new theory, or correct incorrect or misinterpreted results. This book provides details of good experiments, with examples from physics and biology, illustrating the various ways they can be good and the different roles they can play.

In Shifting Standards, Allan Franklin provides an overview of notable experiments in particle physics. Using papers published in Physical Review, the journal of the American Physical Society, as his basis, Franklin details the experiments themselves, their data collection, the events witnessed, and the interpretation of results. From these papers, he distills the dramatic changes to particle physics experimentation from 1894 through 2009. Franklin develops a framework for his analysis, viewing each example according to exclusion and selection of data; possible experimenter bias; details of the experimental apparatus; size of the data set, apparatus, and number of authors; rates of data taking along with analysis and reduction; distinction between ideal and actual experiments; historical accounts of previous experiments; and personal comments and style. From Millikan's tabletop oil-drop experiment to the Compact Muon Solenoid apparatus measuring approximately 4,000 cubic meters (not including accelerators) and employing over 2,000 authors, Franklin's study follows the decade-by-decade evolution of scale and standards in particle physics experimentation. As he shows, where once there were only one or two collaborators, now it literally takes a village. Similar changes are seen in data collection: in 1909 Millikan's data set took 175 oil drops, of which he used 23 to determine the value of e, the charge of the electron; in contrast, the 1988-1992 E791 experiment using the Collider Detector at Fermilab, investigating the hadroproduction of charm quarks, recorded 20 billion events. As we also see, data collection took a quantum leap in the 1950s with the use of computers. Events are now recorded at rates as of a few hundred per second, and analysis rates have progressed similarly. Employing his epistemology of experimentation, Franklin deconstructs each example to view the arguments offered and the correctness of the results. Overall, he finds that despite the metamorphosis of the process, the role of experimentation has remained remarkably consistent through the years: to test theories and provide factual basis for scientific knowledge, to encourage new theories, and to reveal new phenomenon.

This volume summarizes our contemporary understanding of the deconfinement transition in QCD at finite temperature and chemical potential. Questions as to whether a quark-gluon plasma exists in the interior of dense astrophysical objects or which bound-state signals have to be studied in order to unambiguously detect the QCD phase transition(s) in future heavy-ion collision programmes at RHIC and LHC are addressed. Progress in answering these questions requires a fusion of lattice QCD with other nonperturbative approaches and low-energy effective models for QCD. Experts in these fields present in the book their methods and their results in understanding the deconfinement phenomenon.

Consists of 73 articles and added items exclusively for this edition.