Advanced Concepts In Quantum Mechanics

An advanced quantum mechanics textbook that provides a unique pedagogical introduction to high-level topics in the field.

This book comprises the second half of a quantum field theory (QFT) course for graduate students. It gives a concise introduction to advanced concepts that are important for research in elementary particle theory. Topics include the path integral, loop expansion, Feynman rules, various regularization methods, renormalization, running couplings and the renormalization group, fixed points and asymptotic freedom, effective action, Coleman-Weinberg effective potential, fermions, the axial anomaly, QED, gauge fixing, nonabelian gauge theories, unitarity, optical theorem, Slavnov-Taylor identities, beta function of Yang-Mills theory, a heuristic derivation of asymptotic freedom, instantons in SU(N) gauge theory, theta vacua and the strong CP problem. Exercises are included and are intended for advanced graduate students or postdocs seeking to deepen their understanding of QFT.

This book introduces a geometric view of fundamental physics, ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics.

Quantum Mechanics is a fascinating but difficult subject. Mathematics is intimidating and intuition hard to find. The popular books do not go into details of the subject and textbooks are just too hard for self-study. This book aims to bridge the gap between the two. The emphasis of this book is to explain the meaning and intuition behind concepts and mathematics. There is extensive use of analogies from daily life to develop visualization and intuition. This book is well suited for a beginner who has limited physics and mathematics background. The material covered is broad, from elementary Quantum Mechanics to Quantum Field Theory. The topics beyond Quantum Mechanics are introduced as well including Supersymmetry and String Theory.

Taking a conceptual approach to the subject, Concepts in Quantum Mechanics provides complete coverage of both basic and advanced topics. Following in the footsteps of Dirac's classic work Principles of Quantum Mechanics, it explains all themes from first principles.The authors present alternative ways of representing the state of a physical system,

An accessible introduction to advanced quantum theory, this graduate-level textbook focuses on its practical applications rather than mathematical technicalities. It treats real-life examples, from topics ranging from quantum transport to nanotechnology, to equip students with a toolbox of theoretical techniques. Beginning with second quantization, the authors illustrate its use with different condensed matter physics examples. They then explain how to quantize classical fields, with a focus on the electromagnetic field, taking students from Maxwell's equations to photons, coherent states and absorption and emission of photons. Following this is a unique master-level presentation on dissipative quantum mechanics, before the textbook concludes with a short introduction to relativistic quantum mechanics, covering the Dirac equation and a relativistic second quantization formalism. The textbook includes 70 end-of-chapter problems. Solutions to some problems are given at the end of the chapter and full solutions to all problems are available for instructors at www.cambridge.org/9780521761505.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.