Walter Dittrich Knihy

Advanced computational strategies in classical and quantum dynamics are thoroughly explored, offering both fundamental concepts and in-depth discussions on topics such as the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly, and the Berry phase. The text includes well-chosen examples that illustrate key techniques like perturbation theory, canonical transformations, and the action principle, while also demonstrating the application of path integrals in various contexts. This comprehensive approach serves as a valuable resource for graduate students.

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.

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.