Topic
Minisuperspace
About: Minisuperspace is a research topic. Over the lifetime, 1099 publications have been published within this topic receiving 26411 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, the ground state amplitude for a three-manifold is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary.
Abstract: The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}g0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.
3,178 citations
Book•
1 Jan 1995
TL;DR: In this article, the authors present a taxonomy of wormhole taxonomies, from wormhole to time machine, and from wormholes to time machines, with a focus on wormholes.
Abstract: Preface Acknowledgments I. Background: 1. Introduction 2. General Relativity 3. Quantum Field Theory 4. Units and Natural Scales II. History: 5. The Einstein-Rosen Bridge 6. Spacetime Foam 7. The Kerr Wormhole 8. The Cosmological Constant 9. Wormhole Taxonomy 10. Interregnum III. Renaissance: 11. Traversible Wormholes 12. Energy Conditions 13. Engineering Considerations 14. Thin Shells: Fromalism 15. Thin Shells: Wormholes 16. Topological Censorship IV.: Time Travel: 17. Chronology: Basic Notions 18. From Wormhole to Time Machine 19. Response to the Paradoxes V. Quantum Effects 20. Semiclassical Quantum Gravity 21. van Vleck Determinants: Formalism 22. van Vleck Determinants: Wormholes 23. Singularity Structure 24. Minisuperspace Wormholes VI. Reprise: 25. Where We Stand Bibliography Index
1,966 citations
1 Jan 1987
TL;DR: A proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three- geometries as a boundary.
Abstract: The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}g0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.
1,564 citations
Journal Article•
TL;DR: In this paper, the ground state amplitude for a three-manifold is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary.
Abstract: The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}g0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.
953 citations
TL;DR: In this article, the authors provided detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically.
Abstract: We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.
531 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 5 |
| 2023 | 35 |
| 2022 | 194 |
| 2021 | 45 |
| 2020 | 49 |