Degenerate Solutions of General Relativity from Topological Field Theory

@article{Baez1998DegenerateSO,
  title={Degenerate Solutions of General Relativity from Topological Field Theory
},
  author={John C. Baez},
  journal={Communications in Mathematical Physics},
  year={1998},
  volume={193},
  pages={219-231}
}
  • J. Baez
  • Published 1998
  • Physics, Mathematics
  • Communications in Mathematical Physics
Abstract:Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional $BF$ theory on any framed surface Σ embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Σ, while inside this neighborhood the connection A and the field satisfy the equations of 4-dimensional BF theory. Our construction works in any signature and with any… Expand
Universe as a topological defect
Four-dimensional Einstein's general relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of theExpand
Topologically induced gravity
Four-dimensional Einstein's general relativity is shown to arise from a gauge theory for the conformal group, SO(4, 2). The theory is constructed from a topological dimensional reduction of theExpand
Topological and geometric obstructions on Einstein–Hilbert–Palatini theories
Abstract In this article we introduce A -valued Einstein–Hilbert–Palatini functional ( A -EHP) over a n -manifold M , where A is an arbitrary graded algebra, as a generalization of the functionalExpand
Geometric Obstructions on Gravity
These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author's paper arXiv:1808.09249.Expand
Spin Foam Models and the Classical Action Principle
We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theoryExpand
Particles and strings in degenerate metric spaces
We consider relativistic and non-relativistic particles and strings in spaces (or spacetimes) with a degenerate metric. We show that the resulting dynamics is described by a rich structure ofExpand
Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity ∗
This bibliography attempts to give a comprehensive overview of all the literature related to what is known as the Ashtekar- Sen connection and the Rovelli-Smolin loop variables, from which theExpand
Spin foam models
While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define theExpand
A Proposal for the Quantum Theory of Gravity
We propose a model for the quantum theory of gravity. the model has diffeomorphism invariance, a natural length scale, and (plausibly) propagating modes. in the new addendum, we alter the model in aExpand
The particle interpretation of N=1 supersymmetric spin foams
We show that N = 1-supersymmetric BF theory in 3D leads to a supersymmetric spin foam amplitude via a lattice discretization. Furthermore, by analysing the supersymmetric quantum amplitudes, we showExpand

References

SHOWING 1-10 OF 20 REFERENCES
'Sum over surfaces' form of loop quantum gravity
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. WeExpand
Quantum theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. RegulatedExpand
Discreteness of area and volume in quantum gravity [Nucl. Phys. B 442 (1995) 593]
Abstract We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation,Expand
Strings, Loops, Knots and Gauge Fields
The loop representation of quantum gravity has many formal resemblances to a background-free string theory. In fact, its origins lie in attempts to treat the string theory of hadrons as anExpand
New constraints for canonical general relativity
Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariantExpand
Four-dimensional BF theory as a topological quantum field theory
Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFTExpand
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved. The space of solutions is equipped with an inner product that is shownExpand
Knots and quantum gravity: Progress and prospects
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology andExpand
Quantum deformation of quantum gravity
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitableExpand
Spin Networks in Nonperturbative Quantum Gravity
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objectsExpand
...
1
2
...