Quantum geometry with intrinsic local causality

Markopoulou, Fotini; Smolin, Lee

doi:10.1103/physrevd.58.084032

Cited by 79 publications

(163 citation statements)

References 55 publications

(70 reference statements)

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“…2 See [35] for a much earlier suggestion to use surfaces to represent (3 + 1)-dimensional state spaces for quantum gravity.…”

Section: Jhep05(2017)123mentioning

confidence: 99%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.This work has important applications for quantum gravity as well as the theory of topological phases in (3 + 1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably.We in particular show that the fusion bases of the (2 + 1)-dimensional theory lead to a rich set of bases for the (3 + 1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

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“…2 See [35] for a much earlier suggestion to use surfaces to represent (3 + 1)-dimensional state spaces for quantum gravity.…”

Section: Jhep05(2017)123mentioning

confidence: 99%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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“…This suggests that the triple compactification of the Osp(1|32) theory, one limit of which we argued gives rise to the light cone gauge matrix model, may be studied also as a 2 + 1 dimensional topological quantum field theory. A closely related set of structures are the basis of the connection between this model and the background independent approaches to membrane and M theory described in [1,2,3]. This will be discussed elsewhere.…”

Section: Discussionmentioning

confidence: 99%

“…To see the effect of using a cubic action, we may consider a very simple model based on Sp (2). Here the field is given by a matrix…”

Section: Matrix Representation Of Topological Field Theorymentioning

confidence: 99%

“…In the next section we study a simple theory with a cubic action in which the matrices are valued in Sp (2). We show how compactifying it on a circle defines a phase space and that when it is compactified on the three-torus it is equivalent to Chern-Simons theory.…”

Section: Introductionmentioning

confidence: 99%

“…The original motivation for studying this model came from an attempt to simplify a proposal for a background independent formulation of M theory [1], based on a background independent approach to a causal membrane field theory [2,3]. However the model which emerged is quite simple, and so merits a separate presentation.…”

Section: Introductionmentioning

confidence: 99%

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theory as a matrix extension of Chern–Simons theory

Smolin

2000

Nuclear Physics B

Self Cite

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We study a new class of matrix models, the simplest of which is based on an Sp(2) symmetry and has a compactification which is equivalent to Chern-Simons theory on the three-torus. By replacing Sp(2) with the super-algebra Osp(1|32), which has been conjectured to be the full symmetry group of M theory, we arrive at a supercovariant matrix model which appears to contain within it the previously proposed M theory matrix models. There is no background spacetime so that time and dynamics are introduced via compactifications which break the full covariance of the model. Three compactifications are studied corresponding to a hamiltonian quantization in D = 10 + 1, a Lorentz invariant quantization in D = 9 + 1 and a light cone gauge quantization in D = 11 = 9 + 1 + 1. In all cases constraints arise which eliminate certain higher spin fields in terms of lower spin dynamical fields. In the SO(9, 1) invariant compactification we argue that the one loop effective action reduces to the IKKT covariant matrix model. In the light cone gauge compactification the theory contains the standard M theory light cone gauge matrix model, but there appears an additional transverse five form field.

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Loop Quantum Gravity and planck Scale Phenomenology

Smolin

Planck Scale Effects in Astrophysics and Cosmology

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Quantum geometry with intrinsic local causality

Cited by 79 publications

References 55 publications

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

theory as a matrix extension of Chern–Simons theory

Loop Quantum Gravity and planck Scale Phenomenology

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