Quantum Field Theory II (eBook)
by MIKHAIL SHIFMAN (Author)

 63,221 Words
 320 Pages
This textbook grew out of lecture notes the author used in delivering a quantum field theory (QFT) course for students (both in high energy physics and condensed matter) who already had an initial exposure to the subject.
It begins with the path integral method of quantization presented in a systematic and clearcut manner. Perturbation theory is generalized beyond tree level, to include radiative corrections (loops). Renormalization procedures and the Wilsonian renormalization group (RG flow) are discussed, asymptotic freedom of nonAbelian gauge theories is derived, and some applications in Quantum Chromodynamics (QCD) are considered, with a brief digression into the Standard Model (SM). The SM case requires a study of the spontaneous breaking of gauge symmetry, a phenomenon which would be more appropriate to call 'Higgsing of the gauge bosons.' Other regimes attainable in gauge theories are explained as well. In the condensed matter part, the Heisenberg and Ising model are discussed. The present textbook differs from many others in that it is relatively concise and, at the same time, teaches students to carry out actual calculations which they may encounter in QFTrelated applications.
Contents: Yang–Mills Theory
 Yang–Mills Theories (Continued)
 Path Integral Quantization
 Path Integral in Scalar QFT
 Complex Scalar Field and Finite Temperature
 Calculus of Grassmann Numbers and Spinor Fields
 Fermion Fields in Path Integrals
 Gauge Fields in Path Integral: The Simplest Example of QED
 NonAbelian Gauge Fields in Path Integrals
 How to Calculate Charge Renormalization
 Yang–Mills Coupling (Continued)
 What if Vacuum is not Unique
 Condensed Matter Week
 Renormalization Group; RG Flow
 Phases of Yang–Mills Theories
 Anomalous Dimensions. Quark Mass in QCD
 More on χSB. Effective Lagrangians
 Quantum Anomalies
 Quantum Anomalies (Continued)
 'External' Anomalies: Implications
 Divergence of Perturbation Theory at High Orders
 Degenerate (Pre)Vacua and Instantons in QM
 Appendices:
 Nontrivial Topology in the Space of Fields
 Problems
 Brief History of QFT
Readership: Graduate students, and researchers interested in advanced quantum field theory.Yang–Mills Theory;Path Integrals;Gauge Fields;Grassmann Numbers;Scalar QFT0Key Features:
 Combines qualitative explanations of all necessary aspects of modern QFT with the minimal possible set of technicalities
 Includes some important questions such as the divergence of the perturbative series in high orders
 Brief history of QFT is useful for future researchers
 Released: March 12, 2019
 Categories: Science & Nature
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9813234202
 ISBN13: 9789813234208