
A Modern Course in Quantum Field Theory, Volume 2
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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.
Quantum field theory without renormalization theory and without non-perturbative methods is a very formal structure and set of tools. The renormalization group and non-perturbative methods give it profound meaning and purpose. Volume 2 provides a thorough presentation of the standard model, lattice field theory, topological field configurations, supersymmetry and the AdS/CFT correspondence, and it includes a systematic introduction to the functional renormalization group equation with application in noncommutative scalar field theory. Some non-perturbative methods, which allow exact solutions in lower dimensions, or due to the larger amount of symmetries involved, are also discussed.
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Content
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
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