Quantum Field Theory II

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 clear-cut 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 non-Abelian 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 QFT-related applications.
Contents: Yang–Mills TheoryYang–Mills Theories (Continued)Path Integral QuantizationPath Integral in Scalar QFTComplex Scalar Field and Finite TemperatureCalculus of Grassmann Numbers and Spinor FieldsFermion Fields in Path IntegralsGauge Fields in Path Integral: The Simplest Example of QEDNon-Abelian Gauge Fields in Path IntegralsHow to Calculate Charge RenormalizationYang–Mills Coupling (Continued)What if Vacuum is not UniqueCondensed Matter WeekRenormalization Group; RG FlowPhases of Yang–Mills TheoriesAnomalous Dimensions. Quark Mass in QCDMore on χSB. Effective LagrangiansQuantum AnomaliesQuantum Anomalies (Continued)'External' Anomalies: ImplicationsDivergence of Perturbation Theory at High OrdersDegenerate (Pre)Vacua and Instantons in QMAppendices:Nontrivial Topology in the Space of FieldsProblemsBrief 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 technicalitiesIncludes some important questions such as the divergence of the perturbative series in high ordersBrief history of QFT is useful for future researchers