Frozen formalism and canonical quantization in group field theory

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

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Canonical quantization of free fields

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0005 ◽

2021 ◽

pp. 70-98

Author(s):

Iosif L. Buchbinder ◽

Ilya L. Shapiro

Keyword(s):

Field Theory ◽

Quantum Theory ◽

Electromagnetic Fields ◽

Classical Theory ◽

Canonical Quantization ◽

Classical Mechanics ◽

Scalar Fields ◽

Complex Scalar ◽

Spinor Fields ◽

Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

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Ward-constrained melonic renormalization group flow for the rank-four ϕ6 tensorial group field theory

Physical Review D ◽

10.1103/physrevd.100.086009 ◽

2019 ◽

Vol 100 (8) ◽

Cited By ~ 5

Author(s):

Vincent Lahoche ◽

Dine Ousmane Samary

Keyword(s):

Field Theory ◽

Renormalization Group ◽

Renormalization Group Flow ◽

Group Field Theory ◽

Group Flow

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Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

Universe ◽

10.3390/universe5050107 ◽

2019 ◽

Vol 5 (5) ◽

pp. 107 ◽

Cited By ~ 7

Author(s):

Marco de Cesare

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Effective Field ◽

Time Varying ◽

Reconstruction Procedure ◽

Cosmological Background ◽

Bouncing Universe ◽

Physical Information ◽

Group Field Theory ◽

Mimetic Gravity

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power-law expansions of f in different regimes, corresponding e.g., to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational “constants” in the cosmological equations.

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Inhomogeneous universe from group field theory condensate

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2019/02/013 ◽

2019 ◽

Vol 2019 (02) ◽

pp. 013-013 ◽

Cited By ~ 6

Author(s):

Steffen Gielen

Keyword(s):

Field Theory ◽

Inhomogeneous Universe ◽

Group Field Theory

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Holographic Entanglement in Group Field Theory

Universe ◽

10.3390/universe5100211 ◽

2019 ◽

Vol 5 (10) ◽

pp. 211 ◽

Cited By ~ 1

Author(s):

Goffredo Chirco

Keyword(s):

Field Theory ◽

Entanglement Entropy ◽

Bipartite Network ◽

Spin Network ◽

Network State ◽

Tensor Networks ◽

Holographic Entanglement Entropy ◽

Group Field Theory ◽

Network States ◽

Random Tensor

This work is meant as a review summary of a series of recent results concerning the derivation of a holographic entanglement entropy formula for generic open spin network states in the group field theory (GFT) approach to quantum gravity. The statistical group-field computation of the Rényi entropy for a bipartite network state for a simple interacting GFT is reviewed, within a recently proposed dictionary between group field theories and random tensor networks, and with an emphasis on the problem of a consistent characterisation of the entanglement entropy in the GFT second quantisation formalism.

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