<p>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, together with many worked examples throughout the text. This second edition has been enlarged by a new chapter on topological phases in planar electrodynamics and a discussion of the Aharonov-Bohm effect.</p>

Classical and Quantum Dynamics

Science & Math

Dittrich, Walter

Reuter, M.

Mathematics

Springer

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

<p>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.\nThe sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.\nFrom the Back Cover\nGraduate 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.\nThe sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.</p>

Reuter, Martin

<p><p>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.</p> <p>&nbsp;</p> <p>The sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger's source theory treatment of the low-energy &pi;-&rho;-N physics and general relativity, where Riemann's (Einstein's) ideas on space and time and their philosophical implications are discussed. &nbsp;</p> <br /></p>

<p>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.<br />
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.</p>

Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude (SpringerBriefs in History of Science and Technology)

<p>This book describes the historical development of the principle of stationary action from&nbsp; 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. <div>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.</div></p>

The Development of the Action Principle: A Didactic History from Euler-Lagrange to Schwinger (SpringerBriefs in Physics)

Astronomy & Space Science

Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Graduate Texts in Physics)

Computers & Technology

<p><div> <div>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.</div> <div><br /></div> <div>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.</div> </div></p>

<p>In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in 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.<br><br></p>

<p>Classical Yang-mills theory.- Path integral quantization of gauge theories.- Background field methods.- Instantons and ?-Vacua.- Schwinger model (QED)2.- Chiral anomaly in (QCD)2.- Fujikawa's path integral method.- Chiral anomaly in the Schwinger-Symanzik formalism.- Anomalous ward identities à la Wess-Zumino.- Topological aspects of the Wess-Zumino effective action.- Topological baryon number and the Skyrme model.- The Atiyah-Singer index theorem (for the Euclidean Dirac operator).- Chiral anomalies and differential geometry.- Effective gauge theory actions in (2n + 1) dimensions.- Chiral anomaly with gravitational background field.- Vacuum charge in 2n + 1 dimensions.</p>

Selected Topics in Gauge Theories (Lecture Notes in Physics, 244)

Physics

<p>Physics students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here a detailed treatment many worked examples. This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.</p>

Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)

Springer, Verlag

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Books by Dittrich, Walter

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Classical and Quantum Dynamics

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude (SpringerBriefs in History of Science and Technology)

The Development of the Action Principle: A Didactic History from Euler-Lagrange to Schwinger (SpringerBriefs in Physics)

Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Graduate Texts in Physics)

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude (SpringerBriefs in History of Science and Technology)

Selected Topics in Gauge Theories (Lecture Notes in Physics, 244)

Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)