arXiv subjects

Eyo Eyo Ita III

Publications and source records attributed to Eyo Eyo Ita III.

30 records · Page 2Linked to original sources

arXiv2011

Instanton representation of Plebanski gravity. Gravitational instantons from the classical formalism

We present a reformulation of general relativity as a `generalized' Yang--Mills theory of gravity, using a SO(3,C) gauge connection and the self-dual Weyl tensor as dynamical variables. This formulation uses Plebanski's theory as the starting point, and obtains a new action called the instanton representation (IRPG). This paper has yielded a collection of various new results, which show that the IRPG is indeed a fundamentally new approach to GR which should not be confused with existing approaches. Additionally, the IRPG appears to provide a realization of the relation amongst general relativity, Yang--Mills theory and instantons.

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arXiv2011

Instanton representanton of Plebanski gravity. Gravitational coherent states

In this paper we show that the instanton representation of Plebanski gravity exhibits a Hilbert space of harmonic oscillator-like coherent states. We put in place the formalism and carry out the construction of the states, and we elucidate on their physical interpretation. Additionally, we provide an invertible map between the Ashtekar variables and this Hilbert space of states, via the instanton representation. Finally, we compare and constrast our formalism and some of our results with the corresponding ones in loop quantum gravity.

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arXiv2010

Canonical quantization of Plebanski gravity in diagonal variables

In this paper we have carried out a transformation from Ashtekar's theory of GR into a reduced theory where the physical degrees of freedom are explicit. We have performed the canonical analysis, computed the classical dynamics and have performed a quantization on this reduced space, constructing a Hilbert space of states for vanishing cosmological constant. Finally, we have clarified the canonical structure of the dual theory in relation to the original Ashtekar theory.

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arXiv2010

Nonlinear gravitons in 4-D general relativity by expansion about the Kodama state

In this paper we provide a possible realization of Penrose's idea of nonlinear gravitons using a new description of nonmetric general relativity. In the addressal of issues surrounding the normalizability of the Kodama state and its reliability as a ground state for gravity, we expand the theory in fluctuations about the Kodama state. This produces a theory of complex gravity with a well-defined Hilbert space structure, whose quantization we carry out both at the linearized level and in the full nonlinear theory. The results of this paper demonstrate the preservation of the physical degrees of freedom of the full nonlinear theory under linearization, as well provide a Hilbert space of states of the former annihilated by the quantum Hamiltonian constraint.

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arXiv2010

Instanton representation of Plebanski gravity XX. Minisuperspace quantization of gravity coupled to the Klein--Gordon scalar field

In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction potential V, with a direct link to the semiclassical limit below the Planck scale. Additionally, we compute the Hamilton's equations of motion for this model, performing various consistency checks on the quantum theory.

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arXiv2010

Instanton representation of Plebanski gravity XXII. Minisuperspace quantization of gravity coupled to spin 1/2 fermionic fields

In this paper we carry out a quantization of gravity coupled to massless spin 1/2 fermions through the instanton representation of Plebanski gravity. We have constructed a Hilbert space of states for this model, and we have computed the Hamilton's equations of motion. The classical equations appear, at a superficial level, to be consistent with the quantum dynamics of the theory.

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arXiv2010

Instanton representation of Plebanski gravity: XVIII. Quantization and proposed resolution of the Kodama state

In this paper we have constructed a Hilbert space of states solving the initial value constraints of GR in the instanton representation of Plebanski gravity. The states are labelled by two free functions of position constructed from the eigenvalues of the CDJ matrix. This comprises the physical degrees of freedom of GR with a semiclassical limit corresponding to spacetimes of Petrov Type I, D and O. The Hamiltonian constraint in this representation is a hypergeometric differential equation on the states, for which we have provided a closed form solution. Additionally, we have clarified the role of the Kodama state within this Hilbert space structure, which provides a resolution to the issue of its normalizability raised by various authors.

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arXiv2010

Instanton representation of Plebanski gravity: IX. Hamiltonian minisuperspace dynamics in undensitized momentum space variables

In this paper we illustrate the dynamics of the instanton representation in the description of vacuum GR in minisuperspace for undensitized variables. We uncover a new class of general solutions in both the degenerate and the nondegenerate sectors of the theory. Additionally, the individual sectors are preserved under Hamiltonian evolution. Finally, we present an algorithm for constructing general solutions by expansion about the isotropic sector.

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arXiv2008

Generalized Kodama partition functions: A preview into normalizability for the generalized Kodama states

In this paper we outline the computation of the partition function for the generalized Kodama states (GKod) of quantum gravity using the background field method. We show that the coupling constant for GKod is the same dimensionless coupling constant that appears in the partition function of the pure Kodama state (Chern--Simons functional) and argue that the GKod partition function is renormalizable as a loop expansion in direct analogy to Chern--Simons perturbation theory. The GKod partition function contains an infinite set of 1PI vertices uniquely fixed, as a result of the semiclassical-quantum correspondence, by the first-order vertex. This implies the existence of a well-defined effective action for the partition function since the `phase' of the GKod, provided a finite state exists, is equivalent to this effective action. Additionally, the separation of the matter from the gravitational contributions bears a resemblance to the infinite dimensional analogue to Kaluza--Klein theory. Future directions of research include extension of the computations of this paper to the norm of the GKod as well as to examine the analogue of the Chern--Simons Jone's polynomials and link invariants using the GKod as a measure.

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arXiv2008

A brief survey of the renormalizability of four dimensional gravity for generalized Kodama states

We continue the line of research from previous works in assessing the suitability of the pure Kodama state both as a ground state for the generalized Kodama states, as well as characteristic of a good semiclassical limit of general relativity. We briefly introduce the quantum theory of fluctuations about DeSitter spacetime, which enables one to examine some perturbative aspects of the state. Additionally, we also motivate the concept of the cubic tree network, which enables one to view the generalized Kodama states in compact form as a nonlinear transformation of the pure Kodama states parametrized by the matter content of the proper classical limit. It is hoped that this work constitutes a first step in addressing the nonperturbative renormalizability of general relativity in Ashtekar variables. Remaining issues to address, including the analysis of specific matter models, include finiteness and normalizability of the generalized Kodama state as well as reality conditions on the Ashtekar variables, which we relegate to separate works.

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arXiv2008

Finite states in four dimensional quantized gravity

This is the first in a series of papers outlining an algorithm to explicitly construct finite quantum states of the full theory of gravity in Ashtekar variables. The algorithm is based upon extending some properties of a special state, the Kodama state for pure gravity with cosmological term, to matter-coupled models. We then illustrate a presciption for nonperturbatively constructing the generalized Kodama states, in preparation for subsequent works in this series. We also introduce the concept of the semiclassical-quantum correspondence (SQC). We express the quantum constraints of the full theory as a system of equations to be solved for the constituents of the `phase' of the wavefunction. Additionally, we provide a variety of representations of the generalized Kodama states including a generalization of the topological instanton term to include matter fields, for which we present arguments for the field-theoretical analogue of cohomology on infinite dimensional spaces. We demonstrate that the Dirac, reduced phase space and geometric quantization procedures are all equivalent for these generalized Kodama states as a natural consequence of the SQC. We relegate the method of the solution to the constraints and other associated ramifications of the generalized Kodama states to separate works.

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arXiv2008

Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model

In this paper we construct the generalized Kodama state for the case of a Klein--Gordon scalar field coupled to Ashtekar variables in isotropic minisuperspace by a new method. The criterion for finiteness of the state stems from a minisuperspace reduction of the quantized full theory, rather than the conventional techniques of reduction prior to quantization. We then provide a possible route to the reproduction of a semiclassical limit via these states. This is the result of a new principle of the semiclassical-quantum correspondence (SQC), introduced in the first paper in this series. Lastly, we examine the solution to the minisuperspace case at the semiclassical level for an isotropic CDJ matrix neglecting any quantum corrections and examine some of the implications in relation to results from previous authors on semiclassical orbits of spacetime, including inflation. It is suggested that the application of nonperturbative quantum gravity, by way of the SQC, might potentially lead to some predictions testable below the Planck scale.

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