
Book contents
- Frontmatter
- Contents
- Contributors
- Symposium Program
- Papers from both Volumes Classified by Subjects
- Preface
- Dieter Brill: A Spacetime Perspective
- Thawing the Frozen Formalism: The Difference Between Observables and What We Observe
- Jacobi's Action and the Density of States
- Decoherence of Correlation Histories
- The Initial Value Problem in Light of Ashtekar's Variables
- Status Report on an Axiomatic Basis for Functional Integration
- Solution of the Coupled Einstein Constraints On Asymptotically Euclidean Manifolds
- Compact Cauchy Horizons and Cauchy Surfaces
- The Classical Electron
- Gauge (In)variance, Mass and Parity in D=3 Revisited
- Triality, Exceptional Lie Groups and Dirac Operators
- The Reduction of the State Vector and Limitations on Measurement in the Quantum Mechanics of Closed Systems
- Quantum Linearization Instabilities of de Sitter Spacetime
- What is the True Description of Charged Black Holes?
- Limits on the Adiabatic Index in Static Stellar Models
- On the Relativity of Rotation
- Recent Progress and Open Problems in Linearization Stability
- Brill Waves
- You Can't Get There from Here: Constraints on Topology Change
- Time, Measurement and Information Loss in Quantum Cosmology
- Impossible Measurements on Quantum Fields
- A New Condition Implying the Existence of a Constant Mean Curvature Foliation
- Maximal Slices in Stationary Spacetimes with Ergoregions
- (1 + 1)-Dimensional Methods for General Relativity
- Coalescence of Primal Gravity Waves to Make Cosmological Mass Without Matter
- Curriculum Vitae of Dieter Brill
- Ph. D. Theses supervised by Dieter Brill
- List of Publications by Dieter Brill
The Classical Electron
Published online by Cambridge University Press: 06 January 2010
- Frontmatter
- Contents
- Contributors
- Symposium Program
- Papers from both Volumes Classified by Subjects
- Preface
- Dieter Brill: A Spacetime Perspective
- Thawing the Frozen Formalism: The Difference Between Observables and What We Observe
- Jacobi's Action and the Density of States
- Decoherence of Correlation Histories
- The Initial Value Problem in Light of Ashtekar's Variables
- Status Report on an Axiomatic Basis for Functional Integration
- Solution of the Coupled Einstein Constraints On Asymptotically Euclidean Manifolds
- Compact Cauchy Horizons and Cauchy Surfaces
- The Classical Electron
- Gauge (In)variance, Mass and Parity in D=3 Revisited
- Triality, Exceptional Lie Groups and Dirac Operators
- The Reduction of the State Vector and Limitations on Measurement in the Quantum Mechanics of Closed Systems
- Quantum Linearization Instabilities of de Sitter Spacetime
- What is the True Description of Charged Black Holes?
- Limits on the Adiabatic Index in Static Stellar Models
- On the Relativity of Rotation
- Recent Progress and Open Problems in Linearization Stability
- Brill Waves
- You Can't Get There from Here: Constraints on Topology Change
- Time, Measurement and Information Loss in Quantum Cosmology
- Impossible Measurements on Quantum Fields
- A New Condition Implying the Existence of a Constant Mean Curvature Foliation
- Maximal Slices in Stationary Spacetimes with Ergoregions
- (1 + 1)-Dimensional Methods for General Relativity
- Coalescence of Primal Gravity Waves to Make Cosmological Mass Without Matter
- Curriculum Vitae of Dieter Brill
- Ph. D. Theses supervised by Dieter Brill
- List of Publications by Dieter Brill
Summary
We resolve the longstanding paradox that in classical electrodynamics the energy and linear momentum of the Abraham-Lorentz (classical) electron do not transform as 4-vector components under Lorentz transformations. In our treatment these quantities transform properly and remain finite in the point particle limit.
Introduction
In Classical Electrodynamics the energy and linear momentum of the extended classical electron do not transform as components of a 4-vector (Leighton, 1959); also infinities arise in the point charge limit.
Abraham (1905) and Lorentz (1909) proposed the classical model of the electron. Lorentz suggested a model in which the electron consisted of a thin, uniformly charged shell. Poincaré (1909) added a stress in order to stabilize the electron. However, he used an expression for the cohesive stress-energy tensor which led to difficulties (Fermi, 1922; Pais, 1948).
Dirac (1938a, 1938b), Matthison (1931, 1940, 1942) and others have proposed point particle models for the classical electron. The lack of covariance associated with the Abraham-Lorentz model and other extended models of the electron does not arise in such models or in classical models based on non local generalisations of Maxwell electromagnetism; see for example, Bopp (1942), McManus (1948) and Feynmann (1948). Erber (1961) reviews much of the literature on models of the classical electron.
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- Directions in General RelativityProceedings of the 1993 International Symposium, Maryland: Papers in Honor of Dieter Brill, pp. 108 - 113Publisher: Cambridge University PressPrint publication year: 1956