Editorial for the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms”

Carrozza, Sylvain; Gielen, Steffen; Oriti, Daniele

doi:10.3390/universe6010019

Cited by 5 publications

(6 citation statements)

References 30 publications

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“…For a triangulation with N building blocks, the resulting action (75) describes a theory of N coupled particles that carve out a trajectory on the superspace of discrete and selfdual geometries on the lattice. Strikingly similar ideas can be found in group field theory (GFT), which is an approach to quantum gravity where the kinematical wave function for an individual building block is promoted into a second-quantized field operator [47][48][49][50]. In this way, transition amplitudes for simplicial boundary states turn into Feynman amplitudes for an auxiliary quantum field theory on the underlying configuration space, which is a sortof mini-superspace of geometry (in three spatial dimensions, this is usually G 4 /G for gauge groups G = SU (2) or G = SL(2, C)).…”

Section: Outlook and Discussionmentioning

confidence: 70%

Simplicial graviton from selfdual Ashtekar variables

Wieland

2023

Class. Quantum Grav.

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In perturbative gravity, it is straight-forward to characterize the two local degrees of freedom of the gravitational field in terms of a mode expansion of the linearized perturbation. In the non-perturbative regime, we are in a more difficult position. It is not at all obvious how to construct Dirac observables that can separate the gauge orbits. Standard procedures rely on asymptotic boundary conditions or formal Taylor expansions of relational observables. In this paper, we lay out a new non-perturbative lattice approach to tackle the problem in terms of Ashtekar's self-dual formulation. Starting from a simplicial decomposition of space, we introduce a local kinematical phase space at the lattice sites. At each lattice site, we introduce a set of constraints that replace the generators of the hypersurface deformation algebra in the continuum. We show that the discretized constraints close under the Poisson bracket. The resulting reduced phase space describes two complex physical degrees of freedom representing the two radiative modes at the discretized level. The paper concludes with a discussion of the key open problems ahead and the implications for quantum gravity.

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Section: Outlook and Discussionmentioning

confidence: 70%

Simplicial graviton from selfdual Ashtekar variables

Wieland

2023

Class. Quantum Grav.

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“…These equations have to be satisfied for every operator Ô in the GFT Hilbert space. In particular, notice that a state satisfying (10) automatically satisfies the Schwinger-Dyson equation for Ô = . In this sense both choices are approximately equivalent.…”

Section: Gft Dynamicsmentioning

confidence: 99%

“…[34]. There, it was shown that one can derive an equation like (10) by starting with the Hamiltonian constraint of LQG and translating it into a constraint in the Hilbert space of GFT, which can be done given the relation between the Hilbert spaces of both approaches that I have highlighted above. In this sense, one can try to justify the adoption of canonical GFT by appealing to LQG.…”

Section: Gft Dynamicsmentioning

confidence: 99%

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Foundational Issues in Group Field Theory

Mozota Frauca

2024

Found Phys

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In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the amplitudes of certain spin foam models as Feynman amplitudes in a perturbative expansion. However, I argue that it is unclear that this definition of GFTs amounts to something beyond a computational rule for finding these transition amplitudes and that GFT doesn’t seem able to offer any new insight into the foundations of quantum gravity. Then, I move to another formulation of GFT which I call canonical GFT and which uses the standard structures of quantum mechanics. This formulation is of extended use in cosmological applications of GFT, but I argue that it is only heuristically connected with the covariant version and spin foam models. Moreover, I argue that this approach is affected by a version of the problem of time which raises worries about its viability. Therefore, I conclude that there are serious concerns about the justification and interpretation of GFT in either version of it.

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“…Once we have chosen basic variables, here the spinors, it is natural to proceed to a Taylor expansion of the functionals and thus consider polynomial ansatz (of increasing power) for the Hamiltonian H[{z k }]. If the quadratic ansatz, corrected by potential higher order terms, does not yield expected or realistic physics, then this usually indicates that we have made the wrong choice of basic variables and that we should very likely consider a different phase for spin networks (for example, consider a type of condensate of spin networks, as proposed in the group field theory approach [49][50][51]) and the corresponding different boundary data for loop quantum gravity on space-time corners.…”

Section: Spinor Dynamics On the 2 + 1-dimensional Time-like Boundarymentioning

confidence: 99%

Loop quantum gravity boundary dynamics and SL(2,C) gauge theory

Livine¹

2021

Class. Quantum Grav.

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In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3 + 1 space-time dimensions, the boundary theory lives on the 2 + 1-dimensional time-like boundary and is supposed to describe the time evolution of gravitational boundary modes—‘edge modes’—living on the two-dimensional boundary of space, i.e. the space-time corner. We do not analyse the boundary structures of general relativity and their quantization, and focus instead on investigating which boundary theories can be supported by the standard loop quantum gravity formalism and spin network states. Focussing on ‘electric’ excitations—quanta of area—living on the corner, we formulate their dynamics in terms of classical spinor variables and we show that the coupling constants of a polynomial Hamiltonian can be understood as the components of a background metric on the 2 + 1-dimensional time-like boundary. This leads to a conjecture of a deeper correspondence between boundary Hamiltonian and boundary metric states. We further show that one can reformulate the quanta of area data in terms of a connection, transporting the spinors on the boundary surface and whose SU(2) component would define ‘magnetic’ excitations (tangential Ashtekar–Barbero connection), thereby opening the door to writing the loop quantum gravity boundary dynamics as a 2 + 1-dimensional gauge theory.

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Editorial for the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms”

Cited by 5 publications

References 30 publications

Simplicial graviton from selfdual Ashtekar variables

Simplicial graviton from selfdual Ashtekar variables

Foundational Issues in Group Field Theory

Loop quantum gravity boundary dynamics and SL(2,C) gauge theory

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