Loop Quantum Gravity Theory Research Articles

Phenomenology of loop quantum cosmology

After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some long-standing questions in early universe cosmology.

Unstable anisotropic loop quantum cosmology

We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of loop quantum cosmology. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full loop quantum gravity theory and loop quantum cosmology. As a result, one may question the choice of the quantization approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should, in principle, be dictated by the full loop quantum gravity theory.

Spontaneous symmetry breaking in loop quantum gravity

In this paper we investigate the question of how spontaneous symmetry breaking works in the framework of loop quantum gravity and compare it to the results obtained in the case of the Proca field, where we were able to quantize the theory in loop quantum gravity without introducing a Higgs field. We obtained that the Hamiltonian of the two systems is very similar, the only difference is an extra scalar field in the case of spontaneous symmetry breaking. This field can be identified as the field that carries the mass of the vector field. In the quantum regime this becomes a well-defined operator, which turns out to be a self-adjoint operator with continuous spectrum. To calculate the spectrum we used a new representation in the case of scalar fields, which in addition enabled us to rewrite the constraint equations to a finite system of linear partial differential equations. This made it possible to solve part of the constraints explicitly.

Follow the Bouncing Universe

The author examines the theory of loop quantum gravity (loop gravity), which presents an alternative to the big bang theory of universal creation. The history of loop gravity is examined, from the ways in which Albert Einstein's perception of spacetime influenced the theory to its modern applications in quantum mechanics. Also discussed is how concepts such as quantum-gravitational change and thermodynamics influence the theory. INSETS: Mirror, Mirror;REPLACING THE BANG;LOOKING QUITE REPULSIVE;THE THEORY JUST WENT BANG/

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.

A hole revolution, or are we back where we started?

Doubts are raised concerning Rickles’ claim that “an exact analog of the hole argument can be constructed in the loop representation of quantum gravity” [Rickles, D.P. (2005). A new spin on the hole argument. Studies In History and Philosophy of Modern Physics, 36, 415–434].

A discrete-time interpretation of the Planck-Einstein equation

An important conclusion of both string theory and loop quantum gravity theory is that space and time are ultimately discrete. A consequence of discrete space is that there is empty space between the basic elements of space. Analogously, there are empty times between the times where time exists. When time does not exist, it is meaningless to consider the existence of the universe. In this note we consider a discrete-time interpretation of the Planck-Einstein equation and draw a curious conclusion about the real age of the universe.

A new spin on the hole argument

This paper shows how an exact analog of the hole argument can be constructed in the loop representation of quantum gravity. The new argument is based on the embedding of spin-networks in a manifold along with the action of the diffeomorphism constraint on them. I will then briefly discuss the implications of this result vis-à-vis the ontological debate about the nature of space. I argue that the conclusions of many physicists working on loop quantum gravity (e.g., Rovelli and Smolin) that the loop representation uniquely supports relationalism are unfounded, as is the claim of Belot and Earman that quantum gravity might serve to settle the debate one way or the other.

Flat spacetime vacuum in loop quantum gravity

We propose a state in loop quantum gravity theory with zero cosmological constant such that it could be associated with the flat spacetime vacuum solution. This state is constructed by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum general relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin-foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad representation, by defining the corresponding spin network functional integrals as SU(2) quantum group state sums.

Spherically symmetric quantum geometry: states and basic operators

The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory aspects arise. A comparison between a reduced quantization and a derivation of the model from the full theory is presented in detail, with an emphasis on the resulting quantum representation. Similar concepts for Einstein–Rosen waves are discussed briefly.

Loop quantum cosmology: Recent progress

Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum regime. As a consequence, the structure of and the approach to classical singularities are very different from general relativity: The quantum theory is free of singularities, and there are new phenomenological scenarios for the evolution of the very early universe including inflation. We give an overview of the main effects, focussing on recent results obtained by several different groups.

Atoms of space and time.

We perceive space and time to be continuous, but if the amazing theory of loop quantum gravity is correct, they actually come in discrete pieces

Spin-flavour conversion of neutrinos in loop quantum gravity

Loop quantum gravity theory incorporates a new scale length ℒ which may induce a Lorentz invariance breakdown. This scale can be either a universal constant or fixed by the momentum of particles (ℒ ∼ p−1). Effects of the scale parameter ℒ and helicity terms occurring in the dispersion relation of fermions are reviewed in the framework of spin-flip conversion of neutrino flavours.

CERENKOV'S EFFECT AND NEUTRINO OSCILLATIONS IN LOOP QUANTUM GRAVITY

Bounds on the scale parameter ℒ arising in loop quantum gravity theory are derived in the framework of Cerenkov's effect and neutrino oscillations. Assuming that ℒ is an universal constant, we infer ℒ ≳ 10-18 eV -1, a bound compatible with those inferred in different physical context.

Quantization of diffeomorphism-invariant theories with fermions

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P→Σ be a principal G-bundle over space and let F be a vector bundle associated to P whose fiber is a sum of continuous unitary irreducible representations of the compact connected gauge group G, each representation appearing together with its dual. We consider theories whose classical configuration space is A×F, where A is the space of connections on P and F is the space of sections of F, regarded as a collection of Grassmann-valued fermionic fields. We construct the “quantum configuration space” Ā×F̄ as a completion of A×F. Using this, we construct a Hilbert space L2(Ā×F̄) for the quantum theory on which all automorphisms of P act as unitary operators, and determine an explicit “spin network basis” of the subspace L2((Ā×F̄)/Ḡ) consisting of gauge-invariant states. We represent observables constructed from holonomies of the connection along paths together with fermionic fields and their conjugate momenta as operators on L2((Ā×F̄)/Ḡ). We also construct a Hilbert space Hdiff of diffeomorphism-invariant states using the group averaging procedure of Ashtekar, Lewandowski, Marolf, Mourão and Thiemann.

Lattice knot theory and quantum gravity in the loop representation

We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing, and introducing loops, we proceed backwards, setting up constraints in the lattice loop representation and showing that they have appropriate (singular) continuum limits and algebras. The diffeomorphism constraint reproduces the classical algebra in the continuum and has as solutions lattice analogues of usual knot invariants. We discuss some of the invariants stemming from Chern-Simons theory in the lattice context, including the issue of framing. We also present a regularization of the Hamiltonian constraint. We show that two knot invariants from Chern-Simons theory are annihilated by the Hamiltonian constraint through the use of their skein relations, including intersections. We also discuss the issue of intersections with kinks. This paper is the first step towards setting up the loop representation in a rigorous, computable setting.

Degenerate Solutions of General Relativity from Topological Field Theory

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 Sigma embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Sigma, while inside this neighborhood the connection A and the field E = e ^ e satisfy the equations of 4-dimensional BF theory. Moreover, there is a correspondence between these solutions and certain solutions of 2-dimensional BF theory on Sigma. Our construction works in any signature and with any value of the cosmological constant. If M = R x S for some 3-manifold S, at fixed time our solutions typically describe `flux tubes of area': the 3-metric vanishes outside a collection of thickened links embedded in S, while inside these thickened links it is nondegenerate only in the two transverse directions. We comment on the quantization of the theory of solutions of this form and its relation to the loop representation of quantum gravity.

On the relation between the connection and the loop representation of quantum gravity

Using Penrose's binor calculus for SU(2) (SL(2,C)) tensor expressions, a graphical method for the connection representation of Euclidean quantum gravity (real connection) is constructed. It is explicitly shown that: (i) the recently proposed scalar product in the loop-representation coincides with the Ashtekar - Lewandowski cylindrical measure in the space of connections; (ii) it is possible to establish a correspondence between the operators in the connection representation and those in the loop representation. The construction is based on an embedded spin network, the Penrose's graphical method of SU(2) calculus, and the existence of a generalized measure on the space of connections modulo gauge transformations.

The geometry of quantum spin networks

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation of the observable algebra. Operators for area and volume are extended to this theory and, partly, diagonalized. The eigenstates are expressed in terms of q-deformed spin networks. The q-deformation breaks some of the degeneracy of the volume operator so that trivalent spin networks have non-zero volume. These computations are facilitated by use of a technique based on the recoupling theory of , which simplifies the construction of these and other operators through diffeomorphism invariant regularization procedures.

The complete spectrum of the area from recoupling theory in loop quantum gravity

We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did not include the `degenerate' sector, and agrees with the recently computed spectrum of the connection-representation area operator.