A spin network primer

Major, Seth

doi:10.1119/1.19175

Cited by 28 publications

(55 citation statements)

References 11 publications

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“…* Each spin network determines a gauge-invariant functional of the connection, evaluated * For an introduction to spin networks and spin network technology, see [204] and [207].…”

Section: Kinematics and Spin Networkmentioning

confidence: 99%

Quantum gravity: a progress report

2001

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The problem of reconciling general relativity and quantum theory has fascinated and bedeviled physicists for more than 70 years. Despite recent progress in string theory and loop quantum gravity, a complete solution remains out of reach. I review the status of the continuing effort to quantize gravity, emphasizing the underlying conceptual issues and the various attempts to come to grips with them. *

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“…* Each spin network determines a gauge-invariant functional of the connection, evaluated * For an introduction to spin networks and spin network technology, see [204] and [207].…”

Section: Kinematics and Spin Networkmentioning

confidence: 99%

Quantum gravity: a progress report

2001

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“…In short, decoherence will occur whenever clocks are of finite size and therefore subject to quantum fluctuations [GPP04a], leading to an arrow of time in a time-independent theory. Section IV B establishes a connexion between the basis states of the relational theory and "spin networks" introduced by Penrose [Pen71a] as a combinatorial description of geometry and widely studied in the loop formulation of quantum gravity [RS95a,Baez95a] (see also [Majo00a]). It is our hope that the slight distinction between how spin networks arise in our "semi-classically inspired" model and how they are used in loop quantum gravity will yield some new insights on the low energy regime of quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

Toy Model for a Relational Formulation of Quantum Theory

Poulin

2006

Int J Theor Phys

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In the absence of an external frame of reference -i.e. in background independent theories such as general relativity -physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a timesymmetric theory. Moreover, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

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“…We use the binor category of representations [20,21,22] throughout the paper. In this category the crossing diagram is fermionic, which means that the crossing of two lines of odd spin gives a factor of −1.…”

Section: The Eprl Four-simplex Amplitudementioning

confidence: 99%