Area propagator and boosted spin networks in loop quantum gravity

We have considered here the emergence of diffeomorphism symmetry in quantum gravity in the framework of the quantization of a fermion. It is pointed out that a closed loop having the holonomy associated with the SU(2) gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting spin degrees of freedom which appear as SU(2) gauge bundle. During the formation of a loop, a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves q-deformed gauge group SUq(2). This gives rise to q-deformed diffeomorphism and helps to realize diffeomorphism invariance in quantum gravity through a sequence of q-deformed diffeomorphism in the limit q = 1. We can consider adiabatic iteration such that the quasispin associated with the quantum group SUq(2) gradually evolves as the time dependent deformation parameter q changes and in the limit q = 1, we achieve the standard spin. This essentially depicts the evolution of spin network as the loop is being formed and links fermionic degrees of freedom with loop quantum gravity.

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NEW SPIN FOAM MODELS OF QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732305017779 ◽

2005 ◽

Vol 20 (17n18) ◽

pp. 1305-1313

Author(s):

A. MIKOVIĆ

Keyword(s):

General Relativity ◽

Models Of Quantum Gravity ◽

Quantum Gravity ◽

Path Integral ◽

Critical Review ◽

Loop Quantum Gravity ◽

Spin Networks ◽

Spin Foam Models ◽

Spin Foam Model ◽

Spin Foam

We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

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THE PAULI EXCLUSION PRINCIPLE AND SU(2) VERSUS SO(3) IN LOOP QUANTUM GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271803003955 ◽

2003 ◽

Vol 12 (09) ◽

pp. 1729-1736 ◽

Cited By ~ 2

Author(s):

JOHN SWAIN

Keyword(s):

Black Hole ◽

Quantum Gravity ◽

Gauge Group ◽

Loop Quantum Gravity ◽

Pauli Exclusion Principle ◽

Pauli Principle ◽

Exclusion Principle ◽

Spin Networks

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.

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Spin networks and recoupling in loop quantum gravity

Nuclear Physics B - Proceedings Supplements ◽

10.1016/s0920-5632(97)00397-6 ◽

1997 ◽

Vol 57 (1-3) ◽

pp. 251-254 ◽

Cited By ~ 11

Author(s):

R. De Pietri

Keyword(s):

Quantum Gravity ◽

Loop Quantum Gravity ◽

Spin Networks

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New ‘phase’ of quantum gravity

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2006.1904 ◽

2006 ◽

Vol 364 (1849) ◽

pp. 3375-3388 ◽

Cited By ~ 8

Author(s):

Charles H.-T Wang

Keyword(s):

General Relativity ◽

Phase Space ◽

Quantum Gravity ◽

Loop Quantum Gravity ◽

Conformal Symmetry ◽

Quantum Geometry ◽

Spin Networks ◽

Gravitational Fields ◽

The Past ◽

New Phase

The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free (Barbero–Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero–Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.

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A MINIMAL MODEL FOR QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s021773230501683x ◽

2005 ◽

Vol 20 (09) ◽

pp. 645-653 ◽

Cited By ~ 5

Author(s):

PAOLA A. ZIZZI

Keyword(s):

Quantum Gravity ◽

Minimal Model ◽

Loop Quantum Gravity ◽

Quantum Computer ◽

Area Spectrum ◽

Fuzzy Sphere ◽

Spin Networks ◽

Discrete Area ◽

Free Parameters ◽

Minimal Area

We argue that the model of a quantum computer with N qubits on a quantum space background, which is a fuzzy sphere with n = 2N elementary cells, can be viewed as the minimal model for quantum gravity. In fact, it is discrete, has no free parameters, is Lorentz-invariant, naturally realizes the holographic principle, and defines a subset of punctures of spin networks' edges of loop quantum gravity labelled by spins j = 2N-1-½. In this model, the discrete area spectrum of the cells, which is not equally spaced, is given in units of the minimal area of loop quantum gravity (for j = 1/2), and provides a discrete emission spectrum for quantum black holes. When the black hole emits one string of N bits encoded in one of the n cells, its horizon area decreases of an amount equal to the area of one cell.

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