Advanced Modern Physics

The following sections are included:

• Preface

• Contents

The goal of this book is to provide an extension of the previous book Introduction to Modern Physics: Theoretical Foundations, refered to as Vol. I. That volume develops the underlying concepts in twentieth-century physics: quantum mechanics, special relativity, and general relativity. Included in it are applications in atomic, nuclear, particle, and condensed matter physics. It is assumed in Vol. I that readers have had a good calculus-based introductory physics course together with a good course in calculus. Several appendices then provide sufficient background so that, with very few exceptions, the presentation is self-contained. Many of the topics covered in that work are more advanced than in the usual introductory modern physics books. It was the author's intention to provide the best students with an overview of the subject, so that they are aware of the overall picture and can see how things fit together as they progress…

The following sections are included:

• Linear Vector Spaces
  • Three-Dimensional Vectors
  • n-Dimensions

• Hilbert Space
  • Example
  • Definition
  • Relation to Linear Vector Space
  • Abstract State Vector

• Linear Hermitian Operators
  • Eigenfunctions
  • Eigenstates of Position

• Abstract Hilbert Space
  • Inner Product
  • Completeness
  • Linear Hermitian Operators
    • Eigenstates
    • Adjoint Operators
  • Schrödinger Equation
    • Stationary States

• Measurements
  • Coordinate Space
  • Abstract Form
  • Reduction of the Wave Packet
  • Stern-Gerlach Experiment

• Quantum Mechanics Postulates

• Many-Particle Hilbert Space
  • Simple Harmonic Oscillator
  • Bosons
  • Fermions

The following sections are included:

• Translations

• Rotations

• Angular Momentum Operator

• Eigenvalue Spectrum

• Coupling of Angular Momenta

• Recoupling

• Irreducible Tensor Operators

• The Wigner-Eckart Theorem

• Finite Rotations
  • Properties
  • Tensor Operators
  • Wigner-Eckart Theorem (Completed)

• Tensor Products

• Vector Model

The following sections are included:

• Interaction Picture

• Adiabatic Approach

• Û-Operator

• Û-Operator for Finite Times

• The S-Matrix

• Time-Independent Analysis

• Scattering State

• Transition Rate

• Unitarity

• Example: Potential Scattering
  • Green's Function (Propagator)
  • Scattering Wave Function
  • T-matrix
  • Cross Section
  • Unitarity

The following sections are included:

• Particle Mechanics
  • Hamilton's Principle
  • Lagrange's Equations
  • Hamiltonian

• Continuum Mechanics (String–a Review)
  • Lagrangian Density
  • Hamilton's Principle
  • Lagrange's Equation
  • Two-Vectors
  • Momentum Density
  • Hamiltonian Density

• Quantization
  • Particle Mechanics
  • Continuum Mechanics (String)

• Relativistic Field Theory
  • Scalar Field
  • Stress Tensor
  • Dirac Field
  • Noether's Theorem
    • Normal-Ordered Current
  • Electromagnetic Field
  • Interacting Fields (Dirac-Scalar)

The following sections are included:

• Lorentz Invariance

• Rotational Invariance

• Internal Symmetries
  • Isospin–SU(2)
    • Isovector
    • Isospinor
    • Transformation Law
  • Lie Groups
  • Sakata Model–SU(3)
    • Dirac Triplet
    • Scalar Octet
    • Interacting Fields (Dirac-Scalar)

• Phase Invariance
  • Global Phase Invariance
  • Local Phase Invariance

• Yang-Mills Theories

• Chiral Symmetry
  • σ-Model
  • Spontaneous Symmetry Breaking

• Lorentz Transformations

The following sections are included:

• Wick's Theorem

• Example (Dirac-Scalar)
  • Scattering Amplitudes
  • Self-Energies
  • Vacuum Amplitude

• Feynman Diagrams

• Feynman Rules

• Cancellation of Disconnected Diagrams

• Mass Renormalization

The following sections are included:

• Classical Theory

• Hamiltonian

• Quantization

• Photon Propagator

• Second-Order Processes
  • Scattering Amplitudes
  • Self-Energies

• QED With Two Leptons

• Cross Sections
  • e⁻ + μ⁻ → e⁻ + μ⁻
    • Scattering Amplitude
    • Cross Section
    • Traces
    • Cross Section (Continued)
    • Limiting Cases
    • Møller Scattering
  • e⁺ + e⁻ → μ⁺ + μ⁻
    • Scattering Amplitude
    • Cross Section
    • Limiting Cases
    • Colliding Beams

• QED in External Field
  • Nuclear Coulomb Field
  • Bremsstrahlung
  • Pair Production

• Scattering Operator in Order e³

• Feynman Rules for QED
  • General Scattering Operator
  • Feynman Diagrams
  • Feynman Rules
    • Coordinate Space
    • Momentum Space

The following sections are included:

• Example–Scattering in External Field
  • Feynman Diagrams
  • First-Order
  • Vertex Insertion
  • Vacuum Polarization
  • Self-Energy Insertions

• Ward's Identity

• Electron Self-Energy
  • General Form
  • Evaluation
  • Mass Renormalization

• Vertex
  • General Form
  • Ward's Identity
  • Evaluation
  • The Constant L
  • The Infrared Problem
  • Schwinger Moment

• External Lines and Wavefunction Renormalization
  • Cancellation of Divergences

• Vacuum Polarization
  • Evaluation
  • General Form
  • Limiting Cases
  • Insertion
  • Charge Renormalization
  • Charge Strength

• Renormalization Theory
  • Proper Self-Energies
  • Proper Vertex
  • Ward's Identity
  • Ward's Vertex Construct
  • Finite Parts
  • Proof of Renormalization
  • The Renormalization Group

The following sections are included:

• Non-Relativistic Quantum Mechanics with One Degree of Freedom
  • General Relations
  • Infinitesimals
  • Transition Amplitude and Path Integral
  • Classical Limit
  • Superposition
  • Matrix Elements
  • Crucial Theorem of Abers and Lee
  • Functional Derivative
  • Generating Functional

• Many Degrees of Freedom
  • Gaussian Integrals

• Field Theory
  • Fields as Coordinates
  • Measure
  • Generating Functional
  • Convergence
    • Euclidicity Postulate
    • Adiabatic Damping

• Scalar Field
  • Generating Functional for Free Scalar Field
    • Applications
  • Interactions

• Fermions
  • Grassmann Algebra
  • Functional Derivative
  • Functional Integration
  • Integrals
  • Basic Results
  • Generating Functional for Free Dirac Field
    • Applications
  • Interactions (Dirac-Scalar)

• Electromagnetic Field

The following sections are included:

• Interacting Bose System
  • Pseudopotential
  • Special Role of the Ground State
  • Effective Hamiltonian
  • Bogoliubov Transformation
  • Discussion of Results
    • Excitation Spectrum
    • Depletion
    • Ground-State Energy
  • Superfluid ⁴He

• Superconductors
  • Cooper Pairs
  • Bogoliubov-Valatin Transformation
    • Pairing
    • Thermodynamic Potential
    • Wick's Theorem
    • Diagonalization of
    • Gap Equation
  • Discussion of Results
    • Particle Number
    • Ground-State Thermodynamic Potential
    • Ground-State Energy
    • Excitation Spectrum
    • Momentum Operator
    • Quasiparticle Spectrum
    • Calculation of the Energy Gap Δ
    • Quasiparticle Interactions

Please refer to the full text

The following sections are included:

• Appendix A Multipole Analysis of the Radiation Field

• Appendix B Functions of a Complex Variable

• Appendix C Electromagnetic Field

• Appendix D Irreducible Representations of SU(n)

• Appendix E Lorentz Transformations in Quantum Field Theory

• Appendix F Green's Functions and Other Singular Functions

• Appendix G Dimensional Regularization

• Appendix H Path Integrals and the Electromagnetic Field

• Appendix I Metric Conversion

• Bibliography

• Index