Multidisciplinary Approach to Quantum Field Theory, Volume 1: An introduction

Description

This book covers quantum field theory at an introductory level appropriate for graduate students in physics. The first volume aims to allow students to begin their research in fields using quantum field theory, such as particle physics, nuclear physics, cosmology and astrophysics and condensed matter physics. The key areas the book explores include free (noninteracting) fields, field quantization, interacting fields, Feynman diagrams, scattering, cross sections and decay rates; renormalization; symmetry, symmetry breaking and Goldstone bosons. Graduate students studying particle, nuclear, and condensed matter physics are the key audience for this volume. It will also be useful to researchers looking for a modern overview of quantum field theory. Key Features: Emphasizes key concepts and techniques of field theory common across particle physics, nuclear physics, condensed matter physics and cosmology.Examples and problems from many areas of modern physics.Each chapter includes worked examples and exercises within the main body of the text, with more substantial problems at the end of each chapter. PRELIMS.pdf Preface Quantum field theory is ubiquitous in modern physics What should be taught and who learns it is changing How to use this book Acknowledgement Author biography Michael Ogilvie CH001.pdf Chapter 1 Introduction to quantum field theory 1.1 Natural units 1.2 The simple harmonic oscillator in classical mechanics 1.3 The harmonic oscillator in quantum mechanics 1.4 Photons 1.5 Paths to quantum field theory Reference CH002.pdf Chapter 2 Quantum mechanics and path integrals 2.1 Classical mechanics and fields 2.1.1 The Lagrangian formalism 2.1.2 Functional differentiation 2.1.3 Symmetry in classical mechanics 2.1.4 The Hamiltonian formalism 2.2 Quantum mechanics 2.2.1 Time evolution in the Schrödinger picture 2.2.2 The propagator for a free nonrelativistic particle 2.2.3 The Heisenberg representation 2.2.4 Interactions 2.3 The Feynman path integral for one degree of freedom 2.3.1 Defining the path integral 2.3.2 Matrix elements and time ordering 2.3.3 Generating functions 2.3.4 The simple harmonic oscillator 2.3.5 Wick’s theorem 2.3.6 Perturbation theory and Feynman diagrams Problems Bibliography CH003.pdf Chapter 3 Classical fields 3.1 Wave equations in classical mechanics and quantum mechanics 3.2 Special relativity 3.2.1 Geometry of spacetime 3.2.2 Lorentz transformations of fields 3.3 The Lagrangian formalism for fields 3.3.1 The Klein–Gordon equation 3.3.2 Maxwell’s equations 3.3.3 The Schrödinger equation 3.4 Continuous symmetries in classical field theory 3.4.1 Example: translation in space and time 3.5 The Hamiltonian formalism 3.6 Causality Problems CH004.pdf Chapter 4 Free quantum fields 4.1 The Feynman path integral for field theories 4.2 Free scalar fields 4.3 Another approach to the functional integral 4.4 Interpretation of Z[0] for free fields 4.5 Vacuum energy examples 4.5.1 Casimir effect 4.5.2 Energy of field interacting with a static source 4.6 Fock space 4.7 Relativistic invariance and Fock space 4.8 Free quantum fields in Fock space 4.9 The canonical commutation relations and causality 4.10 Equivalence to the functional integral formalism 4.11 Continuous symmetries in quantum field theories Problems Further reading CH005.pdf Chapter 5 Interacting quantum fields 5.1 Perturbation theory and Feynman diagrams 5.2 Feynman diagrams in position space 5.3 Feynman diagrams in momentum space 5.4 Scattering theory 5.5 A toy model of nucleons and pions 5.5.1 The NN and N¯N¯ scattering amplitude 5.5.2 The NN¯ scattering amplitude 5.5.3 Mandelstam variables and crossing symmetry 5.5.4 Four more processes: Nϕ→Nϕ, N¯ϕ→N¯ϕ, NN¯→ϕϕ and ϕϕ→NN¯ 5.6 The CPT theorem 5.7 Cross-sections and decay rates 5.7.1 Decay rates 5.7.2 Cross-sections Problems Reference CH006.pdf Chapter 6 Renormalization 6.1 Mass renormalization 6.2 Coupling constant renormalization 6.3 Field renormalization 6.4 Renormalization: a systematic process 6.5 Renormalizability 6.6 Matrix elements and the LSZ reduction formula Problems Bibliography CH007.pdf Chapter 7 Symmetries and symmetry breaking 7.1 Internal symmetries 7.1.1 Introduction to spontaneous symmetry breaking 7.2 Spontaneous symmetry breaking and perturbation theory 7.3 Broken continuous symmetries and Goldstone bosons 7.3.1 Examples of Goldstone bosons 7.4 Renormalization of models with spontaneous symmetry breaking Problems CH008.pdf Chapter 8 Fermions 8.1 Introduction to the Dirac equation 8.2 Representations of the Lorentz group 8.2.1 The rotation group and its representations 8.2.2 The Lorentz group 8.2.3 Representations of the Lorentz group 8.3 The Dirac equation 8.4 Solutions of the Dirac equation 8.5 The free Dirac field 8.6 Dirac bilinears 8.7 Chiral symmetry and helicity 8.8 Charge conjugation and coupling to the electromagnetic field 8.9 Functional integration for fermions 8.10 Feynman rules and scattering for a Yukawa field theory 8.10.1 Nucleon–nucleon scattering at order g2 8.10.2 Loop diagrams with fermions 8.11 Interpreting the boson and fermion functional determinants 8.12 The linear sigma model of mesons and nucleons Problems