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Quantum Electrodynamics: Atoms, Lasers and Gravity
Pages: 812
- By (author):
- Ulrich D Jentschura (Missouri University of Science and Technology, USA) and
- Gregory S Adkins (Franklin & Marshall College, USA)
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ISBN: 978-981-12-5225-9 (hardcover)
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ISBN: 978-981-12-5227-3 (ebook)
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This book introduces readers to a variety of topics surrounding quantum field theory, notably its role in bound states, laser physics, and the gravitational coupling of Dirac particles. It discusses some rather sophisticated concepts based on detailed derivations which cannot be found elsewhere in the literature.
It is suitable for undergraduates, graduates, and researchers working on general relativity, relativistic atomic physics, quantum electrodynamics, as well as theoretical laser physics.
Sample Chapter(s)
Preface
Chapter 1: Introduction
Contents:
- Introduction
- From Unit Systems for the Microworld to Field Quantization
- Time-Ordered Perturbations
- Bound-Electron Self–Energy and Bethe Logarithm
- Interatomic and Atom-Surface Interactions
- Racah–Wigner Algebra
- Free Dirac Equation
- Dirac Equation for Bound States, Lasers and Gravity
- Electromagnetic Field and Photon Propagators
- Tree-Level and Loop Diagrams, and Renormalization
- Foldy–Wouthuysen Transformation and Lamb Shift
- Relativistic Interactions for Many-Particle and Compound Systems
- Fully Correlated Basis Sets and Helium
- Relativistic Many-Particle Calculations
- Beyond Breit Hamiltonian and On-Shell Form Factors
- Bethe–Salpeter Equation
- NRQED: An Effective Field Theory for Atomic Physics
- Fermionic Determinants and Effective Lagrangians
- Renormalization-Group Equations
Readership: Undergraduates, graduates, and researchers working on general relativity, relativistic atomic physics, quantum electrodynamics, as well as theoretical laser physics.
Free Access
FRONT MATTER
- Pages:i–xxii
https://doi.org/10.1142/9789811252266_fmatter
Preview Abstract
The following sections are included:
- Dedication
- Preface
- Contents
Free Access
Chapter 1: Introduction
- Pages:1–15
https://doi.org/10.1142/9789811252266_0001
Preview Abstract
The following sections are included:
- Accurate Numbers
- Fundamental Constants
- Overview of Chapter Contents
- Miscellaneous Remarks
- Further Thoughts
No Access
Chapter 2: From Unit Systems for the Microworld to Field Quantization
- Pages:17–48
https://doi.org/10.1142/9789811252266_0002
Preview Abstract
The following sections are included:
- Overview
- Atoms and Field Quantization
- Matter Waves and Hamilton–Jacobi Formalism
- Field Quantization as Second Quantization
- Unit Systems Scaled to the Microworld
- Unit Systems and Observation Scales
- Natural Unit System
- Atomic Unit System
- Field Quantization for the Electromagnetic Field
- Quantization of the Free Electromagnetic Field
- Field Operators and Quantized Hamiltonian
- Discretized Formulation of the Field Operators
- Interaction Picture and Phase Conventions
- Field Operators in the Schrödinger and Interaction Pictures
- Integration Measure and Phase Conventions
- Further Thoughts
No Access
Chapter 3: Time-Ordered Perturbations
- Pages:49–74
https://doi.org/10.1142/9789811252266_0003
Preview Abstract
The following sections are included:
- Overview
- Time-Ordered Perturbations and Fermi’s Golden Rule
- Derivation of Fermi’s Golden Rule
- Fermi’s Golden Rule and Nuclear Beta Decay
- Fermi’s Golden Rule and Atomic Decay Rates
- Dynamic Stark Effect
- Way 1: Time-Dependent Perturbation Theory
- Way 2: Quantized Fields
- Way 3: Gell-Mann–Low–Sucher Theorem
- Static Stark Effect and Level Width
- Stark Shift and Large-Order Perturbation Theory
- Quantum Electrodynamics and Large-Order Perturbations
- Further Thoughts
No Access
Chapter 4: Bound-Electron Self–Energy and Bethe Logarithm
- Pages:75–148
https://doi.org/10.1142/9789811252266_0004
Preview Abstract
The following sections are included:
- Overview
- Schrödinger–Coulomb Hamiltonian and Wave Functions
- Spectrum of the Hydrogen Atom and SO (4) Symmetry
- Differential Equations and the Hydrogen Atom
- Schrödinger–Coulomb Bound States
- Schrödinger–Coulomb Virial Theorem
- Schrödinger–Coulomb Continuum States
- Continuum States for a Repulsive Potential
- Schrödinger–Coulomb Green Function in Coordinate Space
- Green Function and Radial Equation
- Solution using Whittaker Functions
- Solution using Laguerre Polynomials
- Green Function and Dynamic Polarizability
- Schrödinger–Coulomb Green Function in Momentum Space
- Free Green Function in Momentum Space
- Toward the SO (4) Symmetry
- Four-Dimensional Spherical Harmonics
- Wave Functions in Momentum Space
- Integral Representation
- Modern Ideas and Bound-State Self–Energy
- Essence of Renormalization
- Overlapping Parameter
- Bound-State Self–Energy: Low-Energy Part
- Length Gauge
- Velocity Gauge
- Calculation of the Bethe Logarithm
- Numerical Values of Bethe Logarithms
- Outline of the High-Energy Part
- Applications of the Developed Formalism
- Electric Dipole Decay and Imaginary Part of Self–Energy
- Magnetic Interactions and Decay Rates
- Higher-Order Terms
- Further Thoughts
No Access
Chapter 5: Interatomic and Atom-Surface Interactions
- Pages:149–189
https://doi.org/10.1142/9789811252266_0005
Preview Abstract
The following sections are included:
- Overview
- Wigner–Brioullin Perturbation Theory
- Spectral Representation of the Green Function
- First-Order and Second-Order Perturbation Theory
- Higher-Order Perturbation Theory (Wigner–Brioullin)
- Application to the Finite-Size Effect
- Master Integrals
- First-Order and Second-Order Finite-Size Effect
- Interatomic Interactions
- Origin of van der Waals and Casimir–Polder Interactions
- Calculation of Interatomic Interactions
- Limit of Large Separation of the Two Atoms
- Nonretarded (van der Waals) Interatomic Interaction
- Interpolating Formula
- Atom-Surface Interactions
- Perfectly Conducting Wall, Long Range
- Dipole Interaction
- Multipole Interactions
- Interactions with a Dielectric Surface
- Further Thoughts
No Access
Chapter 6: Racah–Wigner Algebra
- Pages:191–225
https://doi.org/10.1142/9789811252266_0006
Preview Abstract
The following sections are included:
- Overview
- Clebsch–Gordan Coefficients
- Expansions and Clebsch–Gordan Coefficients
- Matrix Elements and Clebsch–Gordan Coefficients
- Coefficients and Rotations
- Vector Addition or Clebsch–Gordan Coefficients
- Wigner 3j, 6j and 9j Symbols
- Gaunt Coefficients
- Representation of Finite Rotations
- Composed Tensors of Higher Order
- Construction of the Spin-Angular Function
- Construction of the Vector Spherical Harmonic
- Spherical Biharmonic
- Applications of Racah–Wigner Algebra
- Tensor Decomposition of the Light Shift
- Tensorial Decomposition of a Dipole Transition
- Rydberg Electron and Hydrogenlike Core
- Physical Foundation
- Angular Algebra
- Further Thoughts
No Access
Chapter 7: Free Dirac Equation
- Pages:227–263
https://doi.org/10.1142/9789811252266_0007
Preview Abstract
The following sections are included:
- Overview
- Properties of the Free Dirac Equation
- Dirac Equation as the Linearized Klein–Gordon Equation
- Spinor Lorentz Transformation
- Discrete Symmetries
- Overview of the Symmetry Properties
- Solutions of the Free Dirac Equation
- Plane-Wave Solutions of the Dirac Equation
- Dirac Angular Quantum Number
- Angular Momenta and Massless Dirac Equation
- Angular Momenta and Free Dirac Equation
- Quantized Dirac Field and Propagators
- Free Dirac Progator in Feynman’s Formulation
- Feynman Propagator and Green Function
- Free Dirac Propagator in the Angular Momentum Basis
- Further Thoughts
No Access
Chapter 8: Dirac Equation for Bound States, Lasers and Gravity
- Pages:265–319
https://doi.org/10.1142/9789811252266_0008
Preview Abstract
The following sections are included:
- Overview
- Dirac Equation and Coulomb Field
- Electromagnetic Covariant Derivative
- Dirac–Coulomb Bound-State Wave Functions
- Dirac–Coulomb Continuum-State Wave Functions
- Dirac–Coulomb Virial Theorem
- Dirac–Coulomb Propagator
- Dirac–Volkov Equation for Laser Fields
- Dirac–Volkov Solutions for Laser Fields
- Dirac–Volkov Propagator
- Dirac Equation with Coupling to Gravitational Fields
- Metric and Covariant Derivative
- Tetrad Basis and Affine Connection Matrix
- Ricci Rotation Coefficients
- Covariant Derivative of a Spinor
- Covariant Derivative of the Dirac Matrices
- Spin Connection
- Transformation Properties of Rotation Coefficients
- Applications of Gravitational Coupling
- Dirac–Schwarzschild Hamiltonian
- Dirac Adjoint for Curved Space-Times
- Lagrangian and Charge Conjugation
- Further Thoughts
No Access
Chapter 9: Electromagnetic Field and Photon Propagators
- Pages:321–357
https://doi.org/10.1142/9789811252266_0009
Preview Abstract
The following sections are included:
- Overview
- Time Orderings, Field Commutators and Green Functions
- Miscellaneous Fundamental Relations for Green Functions
- Distributions and Fourier Transforms
- Photon Propagator in Coulomb Gauge
- Legendre Transformation and Hamiltonian
- Matching and Photon Propagator
- Photon Propagator in Lorenz Gauge
- Gauge Invariance and Mass of Photon
- Gauge-Fixing Term and Quantization
- Representations of the Photon Propagator
- Photon Propagator in General Gauges
- Construction Principle
- Most General Form and Weyl Gauge
- Gupta–Bleuler Condition
- Wick Theorem and Applications
- Time Ordering and Wick Theorem
- Field Commutators and Current Distributions
- Further Thoughts
No Access
Chapter 10: Tree-Level and Loop Diagrams, and Renormalization
- Pages:359–424
https://doi.org/10.1142/9789811252266_0010
Preview Abstract
The following sections are included:
- Overview
- Tree-Level
- Rutherford Scattering
- Feynman Rules
- Vertex Correction
- Vertex and Pauli–Villars Regularization
- Vertex and Form Factors
- Vertex and Renormalization
- Detour on Dimensional Regularization
- Detour on Feynman Parameterization
- Vertex and Dimensional Regularization
- Vacuum Polarization
- Initial Considerations
- Vacuum Polarization and Dimensional Regularization
- Vacuum Polarization and Coulomb Potential
- Vacuum Polarization and Asymptotics
- Self–Energy Operator
- Self–Energy and Pauli–Villars Regularization
- Self–Energy and Dimensional Regularization
- Renormalization of QED
- Bare and Renormalized Lagrangian
- Renormalization of Vertex and Self–Energy
- Renormalization of Vacuum Polarization
- Compilation of Renormalization Constants
- Forest Formula
- Further Thoughts
No Access
Chapter 11: Foldy–Wouthuysen Transformation and Lamb Shift
- Pages:425–460
https://doi.org/10.1142/9789811252266_0011
Preview Abstract
The following sections are included:
- Overview
- Leading Relativistic Corrections
- Unitary Transformation and Hamiltonian
- Free Dirac Particle
- Transformation in the General Case
- Radiatively Corrected Dirac Hamiltonian
- General Electromagnetic Coupling
- General Particle Hamiltonians
- Applications
- Coulomb Field Coupling
- Magnetic Field Coupling and Electron Moment
- Magnetic Fields and Electrostatic Potentials
- Transition Current
- Nonrelativistic Transition Current and Multipoles
- Dirac Form Factor and Bound-State Radiative Energy Shifts
- Foldy–Wouthuysen Transformation and Form Factors
- High-Energy Part in Photon Mass Regularization
- High-Energy Part in Photon Energy Regularization
- Self–Energy in Dimensional Regularization
- Vacuum Polarization
- Foldy–Wouthuysen Transformation and Gravity
- Further Thoughts
No Access
Chapter 12: Relativistic Interactions for Many-Particle and Compound Systems
- Pages:461–505
https://doi.org/10.1142/9789811252266_0012
Preview Abstract
The following sections are included:
- Overview
- Interatomic Interactions in Covariant Formalism
- General Paradigm of the Matching
- Scattering Amplitudes and Interatomic Interactions
- From the One-Body to the Two-Body Hamiltonian
- Relevant Hamiltonians
- Matching the Two-Particle Interaction Hamiltonian
- Photon Exchange and Breit Hamiltonian
- Breit Hamiltonian for Unequal Particles
- Applications and Generalizations for Many-Particle Systems
- Application to Many-Electron Systems
- Single-Particle Hamiltonian for Arbitrary Spin
- Interaction Hamiltonian for General Spin
- Application to Two-Body Bound Systems
- General Aspects
- Definition of the Lamb Shift
- Application to Hydrogenlike Ions
- Compound System in a Homogeneous Magnetic Field
- Power–Zienau Transformation for a Magnetic Field
- Reduced-Mass Corrections to the Zeeman Effect
- Nuclear Magnetic Shielding
- Further Thoughts
No Access
Chapter 13: Fully Correlated Basis Sets and Helium
- Pages:507–530
https://doi.org/10.1142/9789811252266_0013
Preview Abstract
The following sections are included:
- Overview
- Essential Ingredients for Many-Electron Systems
- Spin Wave Functions
- Two-Body Problem: Center-of-Mass Coordinates
- Three-Body Problem: Mass Polarization
- Relativistic and Radiative Corrections
- Relativistic Corrections
- Derivation of the Helium Lamb Shift
- Numerical Calculation of the Helium Spectrum
- Fully Correlated Basis Sets
- Matrix Elements and Nonorthogonal Basis
- Numerical Results and Technical Issues
- Further Thoughts
No Access
Chapter 14: Relativistic Many-Particle Calculations
- Pages:531–555
https://doi.org/10.1142/9789811252266_0014
Preview Abstract
The following sections are included:
- Overview
- Many-Particle Systems and Hartree–Fock Approximation
- Nonrelativistic Hartree–Fock Approximation
- Implementation and Practical Aspects
- Relativistic Hartree–Fock Methods
- Brown–Ravenhall Disease
- Relativistic Frequency-Dependent Breit Interaction
- Relativistic Hartree–Fock Approximation
- Relativistic Multi–Configurational Approach
- Relativistic Breit Interaction and Spinors
- Subtleties of Nuclear Effects, QED and MCDHF
- Software Packages and Applications
- Systems with a Large Number of Electrons
- Further Thoughts
No Access
Chapter 15: Beyond Breit Hamiltonian and On-Shell Form Factors
- Pages:557–592
https://doi.org/10.1142/9789811252266_0015
Preview Abstract
The following sections are included:
- Overview
- Furry Picture, Scattering Amplitude and Self–Energy
- Furry Picture
- Matching for the Bound-State Self–Energy
- Binding Correction to the Lamb Shift
- Two-Coulomb-Vertex Scattering Amplitude
- Forward Scattering Amplitudes
- Dispersion Relation and Subtractions
- Example Integral
- Final Integration and A50 Coefficient
- Higher-Order Terms
- Relativistic Recoil Correction
- Retardation and Salpeter Correction
- Low-Energy Part and Dipole Approximation
- Middle-Energy Part and Araki–Sucher Distribution
- Seagull Part
- High-Energy Part
- Final Result
- Further Thoughts
No Access
Chapter 16: Bethe–Salpeter Equation
- Pages:593–655
https://doi.org/10.1142/9789811252266_0016
Preview Abstract
The following sections are included:
- Overview
- General Ideas
- Two-Body Bound States and Green Functions
- Questions of Gauge and Transformations
- Reference Kernels and Exact Solutions
- Bound-State Perturbation Theory
- Energy Levels at 𝒪(Zα)4 (BSEQ Approach)
- Relativistic Recoil Correction (BSEQ Approach)
- Exploring Integration Regions
- Method of Regions
- Contribution from the Hard Region
- Soft Contribution from Two Transverse Photons
- Soft Contribution from a Single Transverse Photon
- Ultrasoft Contribution from a Single Transverse Photon
- Sum of the Contributions
- Hyperfine Structure of S States (BSEQ Approach)
- Further Thoughts
No Access
Chapter 17: NRQED: An Effective Field Theory for Atomic Physics
- Pages:657–690
https://doi.org/10.1142/9789811252266_0017
Preview Abstract
The following sections are included:
- Overview
- Basics of NRQED
- NRQED Lagrangian and Feynman Rules
- Matching Coefficients
- Bethe–Salpeter Equation of NRQED
- Applications of NRQED
- Energy Levels at 𝒪(Zα)4 (NRQED Approach)
- Relativistic Recoil Correction (NRQED Approach)
- Hyperfine Structure of S States (NRQED Approach)
- Discussion
- Further Thoughts
No Access
Chapter 18: Fermionic Determinants and Effective Lagrangians
- Pages:691–714
https://doi.org/10.1142/9789811252266_0018
Preview Abstract
The following sections are included:
- Overview
- Derivation of the Heisenberg–Euler Effective Lagrangian
- Heisenberg–Euler Lagrangian for Electric Fields
- Heisenberg–Euler Lagrangian for General Fields
- Application of the Heisenberg–Euler Lagrangian
- Modification of the Speed of Light in Background Fields
- Effective Lagrangian and Wichmann–Kroll Potential
- Further Thoughts
No Access
Chapter 19: Renormalization-Group Equations
- Pages:715–745
https://doi.org/10.1142/9789811252266_0019
Preview Abstract
The following sections are included:
- Orientation and Motivation
- Renormalization on Different Scales
- Renormalization-Group Equations
- Scale Transformations
- From Poor Man’s Scaling to Nontrivial Scaling
- Scale Transformation and Schrödinger Hamiltonian
- Scale Transformation of the Dirac Hamiltonian
- Renormalization Group Transformations
- Functional Equations in the Asymptotic Regime
- Renormalization Group of Callan and Symanzik
- Connection of Callan–Symanzik and Gell-Mann–Low
- RG Equations and Applications
- Effective Action and Renormalization Group
- Brodsky–Lepage–Mackenzie Scale Setting
- Further Thoughts
Free Access
BACK MATTER
- Pages:747–789
https://doi.org/10.1142/9789811252266_bmatter
Preview Abstract
The following sections are included:
- Bibliography
- Index
Ulrich D Jentschura, Diploma/Master in Physics in 1996 from the University of Munich/Max Planck Institute for Quantum Optics in Garching; PhD in 1999 from the University of Technology, Dresden; Habilitation ("PhD de Luxe", Qualification to Advise Others on Doing Independent Research) in 2003 from the University of Technology, Dresden; Group Leader and Heisenberg Fellow at the Max Planck Institute for Nuclear Physics in Heidelberg from 2004–2008; Assistant, Associate and Full Professor at Missouri University of Science and Technology, 2009–2018; Georg Helm Prize of the University of Technology, Dresden, 2000; Heisenberg Prize and Fellowship, 2005; Fellow of the American Physical Society, 2013.
Gregory Adkins is the William G and Elizabeth R Simeral Professor of Physics at Franklin & Marshall College. He earned his BA degree in Mathematics and Physics in 1975 and his PhD degree in Physics in 1981, all from UCLA. He held a postdoctoral position at Princeton University and then joined the faculty of Franklin & Marshall in 1983. He was a visiting researcher at the Institute for Theoretical Physics at the University of California, Santa Barbara and at Caltech. Elected a Fellow of the American Physical Society in 1998. Received the Dewey Award for Outstanding Scholarship in 2000 from Franklin & Marshall and the Lindback Foundation Award for Distinguished Teaching in 2012. He was awarded the American Physical Society Prize to a Faculty Member for Research in an Undergraduate Institution in 2016.
Sample Chapter(s)
Preface
Chapter 1: Introduction
