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.
A Didactic History from Euler-Lagrange to Schwinger
The historical evolution of the principle of stationary action is explored from the 17th to the 20th centuries, highlighting key figures like Bernoulli, Leibniz, Euler, Lagrange, and Laplace. The book delves into its applications in classical physics, including hydrodynamics, electrodynamics, and gravity, while also addressing modern quantum mechanics and quantum field theory. A critical examination of operator versus c-number field theory is included, along with numerous worked examples. It caters to researchers, graduate students, and historians interested in the philosophical implications of physics.
On the Number of Primes Less Than a Given Magnitude
Highlighting the revolutionary contributions of Bernhard Riemann, this book delves into his groundbreaking work on prime numbers, including innovative concepts like analytical continuation and the product formula for entire functions. It provides a thorough analysis of the Riemann zeta-function's zeros and emphasizes the significance of Riemann's ideas in regularizing infinite values within field theory. Through this exploration, the text pays homage to Riemann's lasting influence on mathematical physics and the evolution of mathematical thought.
This book investigates the vacuum of quantum electrodynamics (QED) using the perturbative effective action approach. By probing the vacuum with external perturbations, the system's response can be analyzed after averaging over high energy degrees of freedom, leading to an effective description of vacuum properties akin to those of a classical medium. The focus is on slowly varying fields or soft photons, achieved by integrating out high energy degrees of freedom, specifically electrons, through Schwinger's proper time method. A new representation of the one-loop photon polarization tensor is derived, which couples to all orders with an arbitrary constant electromagnetic field while maintaining dependence on a complete set of invariants. Effective Lagrangians are employed to derive the light cone condition for low-frequency photons in strong fields. The formalism can be extended to various external perturbations, including temperature and Casimir effects. A proof of the "unified formula" for low energy phenomena is presented, describing the refractive indices of various perturbed quantum vacua. In the high energy domain, similarities are noted between a vacuum with a superstrong magnetic field and a magnetized plasma. The book also addresses the measurability of various effects, confirming that no violation of causality is found.
InhaltsverzeichnisUsing Field Theory in Hadron Physics.Composite Hadrons and Relativistic Nuclei.Vacuum Tunneling in Minkowski Space.Hartree Approximation in Field Theory.Two Topics in Eikonal Physics.The Static Potential Energy of a Heavy Quark and Anti Quark.Semiclassical Methods in Field Theory.Lectures on the Relativistic String.and Selected Topics in Source Theory.Confinement, Nonlocal Field Theory, and Electromagnetic Interaction.Supergravity and a Problem Raised by ITS S-Matrix.Quantum Mechanical Corrections to the Classical Maxwell Lagrangian.Spoor of a Fixed Point in QED.Quantum Theory of Synchrotron Radiation.Self-Consistent Quark Bags.