Introduction to Classical and Quantum Field Theory

This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments.
Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way.
Divided into two parts, the first covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing ′real′ physics problems.
Throughout, there are numerous end–of–chapter problems, and a free solutions manual is available for lecturers.


Spis treści:
Acknowledgements.
Introduction to Classical and Quantum Field Theory.
Part One.
1 Introduction.
1.1 What is a Field Theory?
1.2 Basic Mathematical Tools in (Classical) Field Theory.
2 Basics of Classical Field Theory.
2.1 Lagrangian Formulation for Classical Mechanics/Field Theory.
2.2 Conservation Laws in Continuum Field Theory (Noether′s Theorem).
References.
3 Quantization of Classical Field Theories (I).
3.1 Canonical Quantization of Scalar Fields: Bosonic Systems.
3.2 Introduction to Quantum Statistics.
3.3 Path Integral Quantization of Mechanics and Field Theory.
References.
4 Quantization of Classical Field Theories (II).
4.1 Path Integral Quantization in Coherent State Rep resentations of Bosons and Fermions.
4.2 Two Simple Examples of QFT.
4.3 Simple Applications of Path Integral Formulation.
4.4 Symmetry and Conservation Laws in Quantum Field Theory.
References.
Part Two
5 Perturbation Theory, Variational Approach and Correlation Functions.
5.1 Introduction to Perturbation Theory.
5.2 Variational Approach and Perturbation Theory.
5.3 Some General Properties of Correlation Functions.
References.
6 Introduction to Berry Phase and Gauge Theory.
6.1 Introduction to Berry Phase.
6.2 Singular Gauge Potentials and Angular Momentum Quantization.
6.3 Quantization of Electromagnetic Field.
References.
7 Introduction to Effective Field Theory, Phases, and Phase Transitions.
7.1 Introduction to Effective Field Theory: Boltzmann Equation and Fluid Mechanics.
7.2 Landau Theory of Phases and Phase Transitions.
7.3 Other Examples of Effective Classical and Quantum Field Theories.
References.
8 Solitons, Instantons, and Topology in QFT.
8.1 Introduction to Solitons.
8.2 Introduction to Instantons.
8.3 Vortices and Kosterlitz–Thouless Transition.
8.4 Skyrmions and Monopoles.
References.
Part Three: A Few Examples.
9 Simple Boson Liquids: Introduction to Superfluidity.
9.1 Saddle–Point Approximation: Semiclassical Theory for Interacting Bosons.
9.2 Superfluidity.
9.3 Charged Superfluids: Higgs Mechanism and Superconductivity.
9.4 Supersolids.
9.5 A Brief Comment Before Ending.
References.
10 Simple Fermion Liquids: Introduction to Fermi Liquid Theory.
10.1 Single–Particle and Collective Excitations in Fermi Liquids.
10.2 Introduction to Fermi Liquids and Fermi Liquid Theory.
References.
11 Superconductivity: BCS Theory and Beyond.
11.1 BCS Theory for (s–wave) Superconductors: Path Integral Approach.
11.2 BCS Theory for (s–Wave) Superconductors: Fermion Excitations and Hamiltonian Approach.
11.3 Superconductor–Insulator Transition.
References.
12 Introduction to Lattice Gauge Theories.
12.1 Introduction: U(1) and Z<sub>2</sub> Lattice Gauge Theories.
12.2 Strong– and Weak–Coupling Expansions in U(1) Lattice Gauge Theory.
12.3 Instantons in 2+1D U(1) Lattice Gauge Theory.
12.4 Duality Between a Neutral Superfluid and U(1) Gauge Theory Coupled to Charged Bosons.
References.
Appendix: One–Particle Green′s Function in Second–Order Perturbation Theory.
Index.

Nota biograficzna:
Tai–Kai Ng received his Ph.D. degree from Northwestern University, USA, in 1987. In 2001, he accepted a post as Full Professor of Physics at the Hongkong University of Science and Technology, which he still holds. Before that, he held positions at various institutes, among them the Massachusetts Institute of Technology and AT&T Bell Labs. Besides teaching at HKUST, Professor Ng is also involved in secondary and primary school science education, including training school teachers in Investigative Studies in physics and training the Hong Kong International Physics Olympiad team. His research interests include many–body physics and applications of Quantum Field Theory to condensed matter physics. Professor Ng is a member and fellow of the American Physical Society.

Okładka tylna:
This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments.
Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way.
Divided into two parts, the first covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing ′real′ physics problems.
Throughout, there are numerous end–of–chapter problems, and a free solutions manual is available for lecturers.