These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems an...

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor...

This book concludes our exploration of Quantum Mechanics in the Everyone’s Guide Series. Here, we discuss the outstanding mysteries of Quantum Mechanics and the meaning of Reality. Our topics include: EPR paradox Parallel Universes / Many Worlds Bohm’s pilot waves Bell’s Inequality Tests of Locality & Realism Spacetime Quantization & the Planck scale Rovelli’s Relational Quantum Mec...

A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler–Lagrange equations. It introduces Hamilton's principle and us...

Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted ...

The content of the book is based on the lectures on the theory of elasticity, stability, and dynamics of structures. The importance of these disciplines in the preparation of young structural engineers for work in the practice cannot be overemphasized. The university training in such fundamental discipline must seek to build a strong foundation and to illustrate the application of the used methods to practical engineering problems. The solution of a structural engineering problem usually c...

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. Th...

Special relativity is one of the high points of the undergraduate mathematical physics syllabus. Nick Woodhouse writes for those approaching the subject with a background in mathematics: he aims to build on their familiarity with the foundational material and the way of thinking taught in first-year mathematics courses, but not to assume an unreasonable degree of prior knowledge of traditional areas of physical applied mathematics, particularly electromagnetic theory. His book provides mat...

This book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.

Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. A self-contained introduc...

Note: The three volumes are not sequential but rather independent of each other and largely self-contained.Perturbed Evolution has a closer link to Simple Systems than that volume has to Basic Matters, but any reader familiar with the subject matter of a solid introduction to quantum mechanics - such as Dirac's formalism of kets and bras, Schrödinger's and Heisenberg's equations of motion, and the standard examples that can be treated exactly, with harmonic oscillators and hydrogen-like at...

Note: The three volumes are not sequential but rather independent of each other and largely self-contained.The reader of Simple Systems is not expected to be familiar with the material in Basic Matters, but should have the minimal knowledge of a standard brief introduction to quantum mechanics with its typical emphasis on one-dimensional position wave functions. The step to Dirac's more abstract and much more powerful formalism is taken immediately, followed by reviews of quantum kinematic...