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Classical and Quantum Dynamics
Graduate students wishing to become familiar with advanced computational strategies in classical and quantum dynamics will find in the one source both the fundamentals of a standard course as well as a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, illustrated by many worked examples throughout the text. This second edition has been enlarged with a new chapter on topological phases in planar electrodynamics, and a discussion of the Aharonov-Bohm effect.
Climbing the Mountain
This is the first biography ever written on the distinguished physicist Julian Schwinger. Schwinger was one of the most important and influential scientists of the twentieth century. The list of his contributions is staggering, from his early work leading to the Schwinger action principle, Euclidean quantum field theory, and the genesis of the standard model, to later valuable work on magnetic charge and the Casimir effect. He also shared the 1965 Nobel Prize in Physics with Richard Feynman. However, even among physicists, understanding and recognition of his work remains limited. This book by Mehra and Milton, both of whom were personally acquainted with Schwinger, presents a unique portrait that sheds light on both his personality and his work through discussion of his lasting influence on science. Anyone who wishes to gain a deeper understanding of one of the great physicists of this century needs to read this book.
Probing the Quantum Vacuum
This book is devoted to an investigation of the vacuum of quantum elec trodynamics (QED), relying on the perturbative effective action approach. If the vacuum is probed with external perturbations, the response of the system can be analyzed after averaging over the high energy degrees of freedom. This results in an effective description of the properties of the vacuum, which are comparable to the properties of a classical medium. We concentrate primarily on the physics of slowly varying fields or soft photons by integrating out the high energy degrees of freedom, i.e. the elec trons, employing Schwinger's proper time method. We derive a new represen tation of the one loop photon polarization...
The Development of the Action Principle
This book describes the historical development of the principle of stationary action from the 17th to the 20th centuries. Reference is made to the most important contributors to this topic, in particular Bernoullis, Leibniz, Euler, Lagrange and Laplace. The leading theme is how the action principle is applied to problems in classical physics such as hydrodynamics, electrodynamics and gravity, extending also to the modern formulation of quantum mechanics and quantum field theory, especially quantum electrodynamics. A critical analysis of operator versus c-number field theory is given. The book contains many worked examples. In particular, the term "vacuum" is scrutinized.The book is aimed primarily at actively working researchers, graduate students and historians interested in the philosophical interpretation and evolution of physics; in particular, in understanding the action principle and its application to a wide range of natural phenomena.
Quantum Legacy, A: Seminal Papers Of Julian Schwinger
Julian Schwinger (1918-1994) was one of the giants of 20th Century science. He contributed to a broad range of topics in theoretical physics, ranging from classical electrodynamics to quantum mechanics, from nuclear physics through quantum electrodynamics to the general theory of quantum fields. Although his mathematical prowess was legendary, he was fundamentally a phenomenologist. He received many awards, including the first Einstein Prize in 1951, and the Nobel Prize in 1965, which he shared with Richard Feynman and Sin-itiro Tomonaga for the self-consistent formulation of quantum electrodynamics into a practical theory. His more than 70 doctoral students have played a decisive role in the development of science in the second half of this century.This important volume includes many of Schwinger's most important papers, on the above and other topics, such as the theory of angular momentum and the theory of many-body systems. The papers collected here continue to underlie much of the work done by theoretical physicists today.
Reassessing Riemann's Paper
In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann’s only work on prime numbers, including ideas – new at the time – such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the application of Riemann’s zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.
Quantum Gravity and the Functional Renormalization Group
A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Groups, Systems and Many-Body Physics
The authors of the present book share the view that groups and semigroups playa funda mental role in the structure of the complex systems which they are studying. A serious effort was made to implement this point of view by presenting the fundamental concepts pertaining to groups and semigroups before going into the various fields of application. The first two chapters are written in this spirit. The following seven chapters deal with groups in relation to specific systems and lead from basic notions to high-level applications. The systems under study are in all cases characterized by a high degree of complexity as found in the physics of many degrees of freedom and in the theory of automata and systems. In 1977 the authors from the University of Tiibingen (M. Dal Cin, G. John, P. Kramer, A. Rieckers, K. Scheerer and H. Stumpf) organized an International Summer School on Groups and Many-Body Physics. The lectures presented at this School dealt specifically with this interplay of groups and complex systems. The contributions of this book cover the fields which were treated in a condensed form at the Summer School.
