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The review is devoted to an investigation of the physical vacuum properties of quantum electrodynamics (QED), relying on the perturbative effective action approach. By probing the vacuum with external perturbations, its response is analyzed after averaging over the high-energy degrees of freedom. The book is written for scientists active in the field as well as for students who want to become familiar with the more advanced computational strategies of external-field problems which are partly outlined in great detail. Schwinger's proper-time method is the backbone of the book. Many recent results are presented, while others which are widespread in the literature are rederived in a unifying and compact way. The book ranges from full quantum theory to quantum-induced non-linear electrodynamics with its variety of applications to light propagation, photon splitting and light-by-light scattering. A special emphasis is put on systems at finite temperature.
Graduate students who wish to become familiar with advanced
computational strategies in classical and quantum dynamics will
find in this book both the fundamentals of a standard course and a
detailed treatment of the time-dependent oscillator, Chern-Simons
mechanics, the Maslov anomaly and the Berry phase, to name just a
few topics. Well-chosen and detailed examples illustrate
perturbation theory, canonical transformations and the action
principle, and demonstrate the usage of path integrals. The fifth
edition has been revised and enlarged to include chapters on
quantum electrodynamics, in particular, Schwinger's proper time
method and the treatment of classical and quantum mechanics with
Lie brackets and pseudocanonical transformations. It is shown that
operator quantum electrodynamics can be equivalently described with
c-numbers, as demonstrated by calculating the propagation function
for an electron in a prescribed classical electromagnetic field.
Graduate students who want to become familiar with advanced
computational strategies in classical and quantum dynamics will
find here both the fundamentals of a standard course and a detailed
treatment of the time-dependent oscillator, Chern-Simons mechanics,
the Maslov anomaly and the Berry phase, to name a few. Well-chosen
and detailed examples illustrate the perturbation theory, canonical
transformations, the action principle and demonstrate the usage of
path integrals. This new edition has been revised and enlarged with
chapters on quantum electrodynamics, high energy physics, Green's
functions and strong interaction. "This book is a brilliant
exposition of dynamical systems covering the essential aspects and
written in an elegant manner. The book is written in modern
language of mathematics and will ideally cater to the requirements
of graduate and first year Ph.D. students...a wonderful
introduction to any student who wants to do research in any branch
of theoretical Physics." (Indian Journal of Physics)
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 tensor,
coupling to all orders to an arbitrary constant electromagnetic
field, fully maintaining the dependence on the complete set of
invariants. On the basis of effective Lagrangians, we derive the
light cone condition for low frequency photons propagating in
strong fields. Our formalism can be extended to various external
perturbations, such as temperature and Casimir situations. We give
a proof of the "unified formula" for low energy phenom ena that
describes the refractive indices of various perturbed quantum
vacua. In the high energy domain, we observe similarities between a
vacuum with a superstrong magnetic field and a magnetized plasma.
The question of mea surability of the various effects is addressed;
a violation of causality is not found.
Graduate students seeking to become familiar with advanced
computational strategies in classical and quantum dynamics will
find in this book both the fundamentals of a standard course and a
detailed treatment of the time-dependent oscillator, Chern-Simons
mechanics, the Maslov anomaly and the Berry phase, to name just a
few topics. Well-chosen and detailed examples illustrate
perturbation theory, canonical transformations and the action
principle, and demonstrate the usage of path integrals. The sixth
edition has been enlarged to include the Heisenberg-Euler
Lagrangian, Schwinger's source theory treatment of the low-energy -
-N physics and general relativity, where Riemann's (Einstein's)
ideas on space and time and their philosophical implications are
discussed.
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.
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.
This is a collection of lectures and seminars delivered at the
"Symposi- um on Particles and Fields" held at TUbingen University,
West Germany, th from June 20 to July Pt, 1977, on the occasion of
the University's sooth anniversary. We were very fortunate that so
many excellent colleagues from Europe and the U. S. contributed
their ideas to this meeting, whose main pur- pose ist was to cover
a brod spectrum of the various aspects in the current development
of particles and fields, rahter than to focus on a single subject.
It was interesting to see source-, quark-, and string- people side
by side attacking the very same unsolved problems in particle
physics. Exchange of ideas and techniques between the diverse
representatives of field- and particle physics was the principal
goal of the meeting. Last not least, we are most grateful to the
President of our University A. Theis, and his assistant, H. E.
Lang, for the generous support that enabled us to make this
symposium a profitable and pleasant experience for all of us.
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