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A Modern Course in Quantum Field Theory provides a self-contained pedagogical and constructive presentation of quantum field theory. Here, constructive is not meant in the sense of axiomatic field theory, but in the sense that all results must be obtained by an explicit set of calculations from accepted premises by those who start to learn this subject. Written for advanced students, the work provides complete material for a two or three semester course and includes numerous problem exercises, some with detailed solutions.
Preface
Introduction
Standard model
Introduction to lattice field theory
The Wilson and functional renormalization group equations
Noncommutative scalar field theory and its renormalizability
Some exact solutions of quantum field theory
The monopoles and instantons
Introducing supersymmetry
The AdS/CFT correspondence
D Lie algebra representation theory: a primer
D.1 The Cartan Subalgebra
D.2 Roots, Cartan Matrix and Dynkin Diagrams
D.3 Weights, Dynkin Labels and Representations
D.4 Explicit Construction of Lie Algebra Representations
D.4.1 Al = su(l + 1)
D.4.2 Bl = so(2l + 1)
D.4.3 Dl = so(2l)
E On Homotopy theory