Current Algebra And Anomalies

Current algebra remains our most successful analysis of fundamental particle interactions. This collection of surveys on current algebra and anomalies is a successor volume to Lectures on Current Algebra and Its Applications (Princeton Series in Physics, 1972). Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Current algebra and PCAC / S.B. Treiman -- Field theoretic investigations in current algebra / R. Jackiw -- Topological investigations of quantized gauge theories / R. Jackiw -- Chiral anomalies and differential geometry / B. Zumino -- Consistent and covariant anomalies in gauge and gravitational theories / W.A. Bardeen and B. Zumino -- An SU(2) anomaly / E. Witten -- Global aspects of current algebra / E. Witten -- Gravitational anomalies / L. Alvarez-Gaumé and E. Witten -- Current algebra, baryons, and quark confinement / E. Witten -- Skyrmions and QCD / E. Witten

A timely addition to the literature, this volume contains authoritative reviews of three important areas in the physics of elementary particles. Sam B. Treiman, in "Current Algebra and PCAC," reviews the present state of the weak interactions. In "Field Theoretic Investigations in Current Algebra," Roman Jackiw deals with recent developments in current algebra and its applications, giving particular attention to anomalies. David J. Gross covers the high energy inelastic lepton-hadron scattering in his paper, "The High Energy Behavior of Weak and Electromagnetic Interactions." Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of dif feomorphisms of M. In the former case the Lie algebra of the group is the algebra Mg of smooth mappings from M to the Lie algebra gof G. In the latter case the Lie algebra is the algebra Vect M of smooth vector fields on M. However, it turns out that in many applications to field theory and statistical physics one must deal with certain extensions of the above mentioned Lie algebras. In the simplest case M is the unit circle SI, G is a simple finite dimensional Lie group and the central extension of Map( SI, g) is an affine Kac-Moody algebra. The highest weight theory of finite dimensional Lie algebras can be extended to the case of an affine Lie algebra. The important point is that Map(Sl, g) can be split to positive and negative Fourier modes and the finite-dimensional piece g corre sponding to the zero mode.

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

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

These lecture notes discusses the developments both in the theoretical understanding of the physics and mathematics of magnetic monopoles as well as the ways in which they can be detected experimentally.The subject has now become highly interdisciplinary and recent monopole meetings have attracted participants from low temperature physics at one extreme to cosmology at the other.

This is a collection of important papers presented by an international group of outstanding scientists at a seminar on strings and symmetries held in Stony Brook. This volume contains reviews on modern string theory and particle physics, including supersymmetric quantization, supergravity, conformal field theory, topological field theory, string phenomenology, matrix models, and W gravity. This proceedings is both an excellent introduction as well as reference source for researchers.