Structural Aspects Of Quantum Field Theory, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814472700
  • ISBN-13: 9789814472708
  • DDC: 530.14
  • Grade Level Range: College Freshman - College Senior
  • 1596 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013

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This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlins trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Classical Relativistic Field Theory: Kinematical Aspects.
2: Relativistic Free Fields: Bosons.
3: Lagrange Formalism for Fields.
4: Relativistic Invariance.
5: Special Relativity.
6: Relativistic Free Fields: Fermions.
7: Relativistic Free Fields and Spin.
8: Neutral Fermions.
9: Symmetries and Conservation Laws.
10: Differential and Integral Calculus for Anticommuting Variables.
11: Classical Relativistic Field Theory: Dynamical Aspects.
12: Dynamical Principles: Internal Symmetries.
13: Dynamical Principles: External Symmetries.
14: Supergravity.
15: Cosmology.
16: Relativistic Quantum Field Theory: Operator Methods.
17: Quantization of Free Fields.
18: Quantum Mechanical Perturbation Theory.
19: Perturbative Quantum Electrodynamics.
20: Nonrelativistic Quantum Mechanics: Functional Integral Methods.
21: Path Integral Quantization.
22: Path Integral Quantization of the Harmonic Oscillator.
23: Expectation Values of Operators.
24: Perturbative Methods.
25: Nonperturbative Methods.
26: Holomorphic Quantization.
27: Ghost Fermions.
28: Relativistic Quantum Field Theory: Functional Integral Methods.
29: Quantum Fields on a Lattice.
30: Self Interacting Bosonic Quantum Field.
31: Quantum Electrodynamics.
32: Quantum Chromodynamics.
33: Quantum Field Theory at Nonzero Temperature.
34: Nonrelativistic Second Quantization.
35: Quantum Statistical Mechanics.
36: Grand Canonical Ensemble.
37: Bose-Einstein Condensation.
38: Superconductivity.
39: Relativistic Quantum Field Theory at Nonzero Temperature.
40: Fractional Quantum Hall Effect.
Half Title Page.
Title Page.
1: Symmetries and Canonical Formalism.
2: Hamiltonian Formalism and Symplectic Geometry.
3: Conventional Symmetries.
4: Accidental Symmetries.
5: Anomalous Symmetries.
6: Gauge Symmetries and Constrained Systems.
7: Constrained Systems and Symplectic Reduction.
8: Quantum Reduction of Constrained Systems.
9: BRS Quantization of Constrained Systems.
10: Weyl Quantization.
11: Weyl Quantization of Bosons.
12: Weyl Quantization of Bosons and Canonical Transformations.
13: Geometric Quantization and Spin.
14: Weyl Quantization of Fermions.
15: Anomalies in Quantum Field Theory.
16: Anomalies and Index Theorems.
17: Integrated Anomalies.
18: Noncommutative Geometry.
19: Noncommutative Geometry: Algebraic Tools.
20: Noncommutative Geometry: Analytic Tools.
21: Noncommutative Geometry: Particle Physics.
22: A Glance at Noncommutative Quantum Field Theory.
23: Quantum Groups.
24: Hopf Algebras.
25: Quasitriangular Hopf Algebras.
26: Quantum Groups: Basic Example.
27: Noncommutative Geometry and Quantum Groups.
28: Quantum Groups and the Noncommutative Torus.
29: Quantum Hall Effect with Realistic Boundary Conditions.