A First Book of Quantum Field Theory

A First Book of Quantum Field Theory

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$69.95
ISBN 9780849309779
Cat# NA0977
 
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Features

  • Requires no prior knowledge of the subject, only a familiarity with special relativity and quantum mechanics
  • Includes a review of classical field theory and a brief introduction to group theory
  • Presents the P, T, C transformations in a representation-independent way, offering a general formulation useful in a variety of contexts
  • Presents exercise problems as they are relevant to the material, not just at the end of each chapter
  • Summary

    For more than 50 years we have known that quantum field theory is necessary for describing precision experiments involving electromagnetic interactions. More recently it has become clear that it also describes weak and strong interactions, and, in fact, produces an appropriate framework for describing a wide class of phenomena in the energy range covered by all experiments to date.

    A First Book of Quantum Field Theory introduces the subject as an elegant yet relatively simple piece of machinery with a broad range of applications. Although many introductory textbooks approach the subject with description of the electron and the photon as their goal, this treatment takes a rather unique approach through decay processes, which are, in some ways, simpler than scattering processes. Using decay processes allows the authors to introduce the basic machinery of Feynman diagrams even before addressing the quantization of spin-1 fields.

    With clear, engaging prose, strategically placed exercises, and canonical quantization employed throughout the book, A First Book of Quantum Field Theory offers a systematic, straightforward treatment ideal for advanced undergraduate and beginning post-graduate students. Readers will not only grasp the crucial concepts and the tools fundamental to the subject, but they will also discover both its elegance and its utility.

    Table of Contents

    PRELIMINARIES
    Why Quantum Field Theory
    Creation and Annihilation Operators
    Special Relativity
    Space and Time in Relativistic Quantum Theory
    Natural Units
    CLASSICAL FIELD THEORY
    A quick review of particle mechanics
    Euler-Lagrange Equations in Field Theory
    Hamiltonian Formalism
    Noether's Theorem
    QUANTIZATION OF SCALAR FIELDS
    Equation of Motion
    The Field and its Canonical Quantization
    Fourier Decomposition of the Field
    Ground State of the Hamiltonian and Normal Ordering
    Fock Space
    Complex Scalar Field
    Propagator
    QUANTIZATION OF DIRAC FIELDS
    Dirac Hamiltonian
    Dirac Equation
    Plane Wave Solutions of Dirac Equation
    Projection Operators
    Lagrangian for a Dirac Field
    FourIer Decomposition of the Field
    Propagator
    THE S-MATRIX EXPANSION
    Examples of Interactions
    Evolution Operator
    S-Matrix
    Wick's Theorem
    FROM WICK EXPANSION TO FEYNMAN DIAGRAMS
    Yukawa Interaction: Decay of a Scalar
    Normalized States
    Sample Calculation of a Matrix Element
    Another Example: Fermion Scattering
    Feynman Amplitude
    Feynman Rules
    Virtual Particles
    Amplitudes which are not S-Matrix Elements
    CROSS SECTIONS AND DECAY RATES
    Decay Rate
    Example of Decay Rate Calculation
    Scattering Cross Section
    Generalities of 2-to-2 Scattering
    Inelastic Scattering with 4-Fermion Interaction
    Mandelstam Variables
    QUANTUM ELECTRODYNAMICS
    Local Gauge Invariance
    Interaction Hamiltonian
    Lower Order Processes
    Electron-Electron Scattering
    Electron-Positron Scattering
    e-e+®m-m+
    Consequence of Gauge Invariance
    Compton Scattering
    Scattering by an External Field
    Bremmsstrahlung
    P, T, C, AND THEIR COMBINATIONS
    Motivations from Classical Physics
    Parity
    Charge Conjugation
    Time Reversal
    CP
    CPT
    ELECTROMAGNETIC FORM FACTORS
    General Electromagnetic Vertex
    Physical Interpretation of Form Factors
    Anomalous Magnetic Moment of the electron
    Charge Form Factor
    Electron-Proton Scattering
    RENORMALIZATION
    Degree of Divergence of a Diagram
    Specific Examples in QED
    Outline of the Program
    Ward-Takahashi Identity
    General Forms for Divergent Amplitudes
    Regularization of Self-Energy Diagrams
    Counterterms
    Full Lagrangian
    Observable Effects of Renormalization
    SYMMETRIES AND SYMMETRY BREAKING
    Classification of Symmetries
    Groups and Symmetries
    Approximate Symmetries
    Spontaneous Breaking of Symmetries
    Goldstone's Theorem
    Higgs Mechanism
    YANG-MILLS THEORY OF NON-ABELIAN GAUGE FIELDS
    Gauge Fields of Non-Abelian Symmetry
    Pure Gauge Lagrangian
    Interactions of Non-Abelian Gauge Fields
    Equations of Motion and Conserved Currents
    Quantization of Non-Abelian Gauge Fields
    Quantum Chromodynamics
    STANDARD ELECTROWEAK THEORY
    Gauge Group
    Spontaneous Symmetry Breaking
    Fermions in the Theory
    Gauge Boson Decay
    Scattering Processes
    Propagator for Unstable Particles
    Global Symmetries of the Model
    APPENDIX: Useful Formulas
    INDEX

     
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