Directions in General Relativity 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
Decoherence of Correlation Histories
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
Abstract
We use a λΦ4 scalar quantum field theory to illustrate a new approach to the study of quantum to classical transition. In this approach, the decoherence functional is employed to assign probabilities to consistent histories defined in terms of correlations among the fields at separate points, rather than the field itself. We present expressions for the quantum amplitudes associated with such histories, as well as for the decoherence functional between two of them. The dynamics of an individual consistent history may be described by a Langevintype equation, which we derive.
Dedicated to Professor Brill on the occasion of his sixtieth birthday, August 1993
Introduction
Interpretations of Quantum Mechanics and Paradigms of Statistical Mechanics
This paper attempts to bring together two basic concepts, one from the foundations of statistical mechanics and the other from the foundations of quantum mechanics, for the purpose of addressing two basic issues in physics:
the quantum to classical transition, and
the quantum origin of stochastic dynamics.
Both issues draw in the interlaced effects of dissipation, decoherence, noise, and fluctuation. A central concern is the role played by coarse-graining —the naturalness of its choice, the effectiveness of its implementation and the relevance of its consequences.
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- Directions in General RelativityProceedings of the 1993 International Symposium, Maryland: Papers in Honor of Dieter Brill, pp. 38 - 65Publisher: Cambridge University PressPrint publication year: 1956
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