An Introduction To Quantum Field Theory


Book Description

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.



















Physics Briefs


Book Description




Fields and Particles


Book Description

This volume contains the written versions of invited lectures presented at the 29th "Internationale Universitatswochen fiir Kernphysik" in Schladming, Aus tria, in March 1990. The generous support of our sponsors, the Austrian Ministry of Science and Research, the Government of Styria, and others, made it possible to invite expert lecturers. In choosing the topics of the course we have tried to select some of the currently most fiercely debated aspects of quantum field theory. It is a pleasure for us to thank all the speakers for their excellent presentations and their efforts in preparing the lecture notes. After the school the lecture notes were revised by the authors and partly rewritten ~n '!EX. We are also indebted to Mrs. Neuhold for the careful typing of those notes which we did not receive in '!EX. Graz, Austria H. Mitter July 1990 W. Schweiger Contents An Introduction to Integrable Models and Conformal Field Theory By H. Grosse (With 6 Figures) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 1. Introduction ............................................. . 1 1.1 Continuous Integrable Models .......................... . 1 1.2 "Solvable" Models of Statistical Physics ................. . 2 1.3 The Yang-Baxter Relation ............................. . 3 1.4 Braids and I(nots .................................... . 3 1.5 Confonnal Field Theory d = 2 ......................... . 3 2. Integrable Continuum Models - The Inverse Scattering Method - Solitons .................... . 4 2.1 A General Scheme for Solving (Linear) Problems ......... . 4 2.2 The Direct Step ...................................... . 6 2.3 The Inverse Step ..................................... .




No-Nonsense Quantum Field Theory


Book Description

Learning quantum field theory doesn’t have to be hard What if there were a book that allowed you to see the whole picture and not just tiny parts of it? Thoughts like this are the reason that No-Nonsense Quantum Field Theory now exists. What will you learn from this book? Get to know all fundamental concepts — Grasp what a quantum field is, why we use propagators to describe its behavior, and how Feynman diagrams help us to make sense of field interactions. Learn to describe quantum field theory mathematically — Understand the meaning and origin of the most important equations: the Klein-Gordon equation, the Dirac equation, the Proca equation, the Maxwell equations, and the canonical commutation/anticommutation relations. Master important quantum field theory interactions — Read fully annotated, step-by-step calculations and understand the general algorithm we use to particle interactions. Get an understanding you can be proud of —Learn about advanced topics like renormalization and regularization, spontaneous symmetry breaking, the renormalization group equations, non-perturbative phenomena, and effective field models. No-Nonsense Quantum Field Theory is one the most student-friendly book on quantum field theory ever written. Here’s why. First of all, it's nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”. Each chapter, each section, and each page focuses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each equation comes from. The book ruthlessly focuses on the fundamentals and makes sure you’ll understand them in detail. The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook In total, the book contains more than 100 illustrations that help you understand the most important concepts visually. In each chapter, you’ll find fully annotated equations and calculations are done carefully step-by-step. This makes it much easier to understand what’s going on. Whenever a concept is used that was already introduced previously there is a short sidenote that reminds you where it was first introduced and often recites the main points. In addition, there are summaries at the beginning of each chapter that make sure you won’t get lost.




Noncommutative Geometry, Quantum Fields and Motives


Book Description

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.