Main publications. Abstracts and contents of the monographs

The Problems of Quantum Electrodynamics

of the Vacuum, Dispersive Media and Strong Fields

V.P. Oleinik and I.V. Belousov

Kishinev, Shtiintsa, 1983, 256 p.

Edited by Professor V.S. Mashkevich

In the monograph “The Problems of Quantum Electrodynamics of the Vacuum, Dispersive Media and Strong fields” by V.P. Oleinik and I.V. Belousov a new approach to the quantum electrodynamics taking into account the energy level width of dressed particles is formulated and developed. As an application the electron-positron pair creation in external fields is considered. The Hamiltonian theory of interacting electromagnetic and. electron-positron fields is proposed, both in unbounded absorptive dispersive media and in media separated from the vacuum by plane boundary. Quasi-energy spectrum of collective excitations of charge carriers in periodic in time external fields of various configurations is investigated and quantum processes occurring in these fields are considered. Tunnel effects in electric fields are discussed.

The book is based on the original authors’ investigations and addressed to those scientists and senior students who are interested in fundamentals and applications of quantum physics.

CONTENTS

Preface

Notation

Chapter I. QUANTUM ELECTRODYNAMICS OF THE VACUUM

§ 1. Main Ideas and Results

§ 2. Modified Schwinger-Dyson Equations

2.1. Transition Amplitudes and Average Values

2.2. Generalized Green Functions

§ 3. External Field Model

3.1. Generalized and Feynman’s Green Function

3.2. Homogeneous Electric Field

3.3. Green Function Representation in Terms of Reverse Operator

3.4. Transition Amplitudes

§ 4. Particle’s “Dressing”

4.1. Wave Function of a “Dressed” Particle

4.2. “Vacuum Tail” of Electron and Photon

4.3. Lamb Shift of Energy Levels

4.4. Vacuum Current Oscillations

§ 5. Modified Polarization and Mass Operators

5.1. Polarization Operator in a Plane Wave Field

5.2. Mass Operator in a Plane Wave Field

5.3. Polarization Operator in Homogeneous Electric Field

§ 6. Dynamics of Photon in Crossed Field

6.1. Polarization Operator and its Spectral Representation

6.2. Commutative Function and the “Vacuum Tail” of Photon

6.3. Frequency Functions

§ 7. Dynamics of Electron in Crossed Field

7.1. Mass Operator and its Spectral Representation

7.2. Commutative Function and the “Vacuum Tail” of Electron

7.3. Frequency Functions

§ 8. Creation of Electron-Positron Pairs and Emission of Photons

8.1. General Formula for the Mean Number of Pairs

8.2. Emission of Photons

8.3. Pair Creation in Crossed Field

§ 9. Functional Formulation of the Equations for Generalized Green Functions and Functional Integrals

9.1. Generating Functional

9.2. Functional Equations

9.3. Counterterms

9.4. Green Function as a Functional Integral

Chapter II. HAMILTONIAN ELECTRODYNAMICS OF DISPERSIVE MEDIA

§ 1. Physical Particles as Open Systems

§ 2. Classical Mechanics of Damped Oscillator

2.1. Morse-Feshbach Lagrangian Function

2.2. Alternative Formulations

§ 3. Quantum Mechanics of Damped Oscillator

3.1. Quantization of Oscillator

3.2. Ket-Vectors

3.3. Coordinate Representation

3.4. Limit Transition

3.5. Physical Interpretation

§ 4. Electrodynamics of Absorptive Dispersive Medium

4.1. Lagrangian Function

4.2. Hamiltonian Function and Quantization

4.3. Vavilov-Čherenkov Effect

4.4. Application to Electrodynamics of the Vacuum

§ 5. Energy Characteristics of Electromagnetic Field in a Non-Absorptive Dispersive Medium

5.1. Lagrangian and Hamiltonian Functions

5.2. Energy and Effective Potential

5.3. Field Quantization and Dirac Equation for an Extraneous Electron in Medium

§ 6. Electrodynamics of the Dispersive Medium Separated from the Vacuum by a Plane Boundary

6.1. Transformation of the Equations for to the First Order Equations

6.2. Transformation of the Equations for and to the First Order Equations

6.3. Peculiarities of the Non-Absorptive Medium Model ()

6.4. Lagrangian and Hamiltonian Functions

§ 7. Emission of Electrons out of the Potential Well and Creation of Electron-Positron Pairs in Electric Field

7.1. Emission of Electrons

7.2. Creation of Electron-Positron Pairs

Chapter III. Quantum Processes in INTENSE ELECTROMAGNETIC FIELDS

§ 1. Simple Model of Electromagnetic Interaction

§ 2. Stimulated Compton Effect in the Intense Electromagnetic Field of a Plane Monochromatic Wave

2.1. Wave Functions and Green Functions of Electrons

2.2 Intensity-Dependent Frequency Shift of a Photon Emitted by Electron in Stimulated Compton Effect

§ 3. Quantum Processes Relativity in Intense Electromagnetic Field

3.1. Stimulated Compton Effect

3.2. Interacting Fields and Particle Scattering Experiments in Different Reference Frames

§ 4. Resonant MÆller Scattering of Electrons in Intense Electromagnetic Field

4.1. Differential Effective Cross-Section of Resonant MÆller Scattering

4.2. Integral Cross-Section of the MÆller Scattering and Effective Interaction of Electrons in Intense Electromagnetic Field

§ 5. Resonant Compton Scattering in Intense Electromagnetic Field

5.1. Frequency Characteristics of Compton Scattering

5.2. Integral Effective Cross-Section of Compton Scattering

§ 6. Electron-Positron Pair Creation by a Photon in the Field of Plane Electromagnetic Wave and Constant Homogeneous Magnetic Field

6.1. Quasi-Energy - Quasi-Momentum Conservation Laws and their Consequences

6.2. Pair Creation Probability

§ 7. Radiative and Nonradiative Quantum Transitions of Electron in the Field of Plane Electromagnetic Wave and Constant Homogeneous Magnetic Field

7.1. Nonradiative Transitions

7.2. Stimulated Compton Effect in Constant Homogeneous Magnetic Field

REFERENCES

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