Superposition induced topology changes in quantum gravity (original) (raw)

Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

Physical Review Letters

In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

Quantum gravity in terms of topological observables

Arxiv preprint hep-th/0501191, 2005

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G N ewton Λ) and extremely small 10 −120 . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory. *

Fe b 20 05 Quantum gravity in terms of topological observables

2006

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (GNewtonΛ) and extremely small 10 . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory.

A Starodubtsev, Quantum gravity in terms of topological observables

2013

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (GNewtonΛ) and extremely small 10 −120. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory. 1

Topology change and quantum physics

Nuclear Physics B, 1995

The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-stafistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized.

Topology change in classical and quantum gravity

Classical and Quantum Gravity, 1991

In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular Lorentzian metric and how these difficulties can be circumvented in the Euclidean approach to quantum gravity. Originally circulated as Topology change in classical and quantum gravity.

Gauge theory of quantum gravity

2014

The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great challenge in physics. Here we present an alternative construction of quantum gravity in which the quantum gravitational degrees of freedom are described by the non-Abelian gauge fields characterizing topological non-triviality of the space-time. The quantum dynamics of the space-time thus corresponds to the superposition of the distinct topological states. Its unitary time evolution is described by the path integral approach. This result will also be suggested to solve some major problems in physics of the black holes.

Quantum states of topologically massive electrodynamics and gravity

Journal of Physics A: Mathematical and General, 1996

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a regularization phase which depends on the spin. This is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scalar product on such a Hilbert space. The physical properties of the states are analyzed defining creation and annihilation operators. For both theories, a canonical and covariant quantization procedure is developed. The higher order derivatives in the gravitational lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincaré algebra is guaranteed by the infrared-finiteness of the states which is related to the spin of the excitations through the regularization phase. Such a phase may have interesting physical consequences.

Geometry, Topology and Quantum Field Theory

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Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach

2011

These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants (c,G,\Lambda,\hbar) enter as deformation parameters. The classical situation is summarised, where solutions can be characterised in terms of model spacetimes (which depend on c and \Lambda), together with global identifications via elements of the corresponding isometry groups. The quantum theory may be viewed as a deformation of this picture, with quantum groups replacing the local isometry groups, and non-commutative spacetimes replacing the classical model spacetimes. This point of view is explained, and open issues are sketched.