Group field theory (GFT) is a
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
in which the base manifold is taken to be a
Lie group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...
. It is closely related to
background independent Background independence is a condition in theoretical physics that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means tha ...
quantum gravity approaches such as
loop quantum gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
, the
spin foam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structur ...
formalism and
causal dynamical triangulation
Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent.
This means that it does not assum ...
. It can be shown that its perturbative expansion can be interpreted as
spin foam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structur ...
s and
simplicial pseudo-manifolds (depending on the representation of the fields). Thus, its
partition function defines a
non-perturbative
In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. An example is the function
: f(x) = e^,
which does not have a Taylor series at ''x'' = 0. Every coefficient of the Taylor ...
sum over all simplicial topologies and geometries, giving a path integral formulation of
quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebr ...
.
See also
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Shape dynamics
In theoretical physics, shape dynamics is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general ...
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Causal Sets
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Fractal cosmology
In physical cosmology, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales (see also: multif ...
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Loop quantum gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
*
Planck scale
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Quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
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Regge calculus In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961. Available ...
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
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Simplicial manifold
In physics, the term simplicial manifold commonly refers to one of several loosely defined objects, commonly appearing in the study of Regge calculus. These objects combine attributes of a simplex with those of a manifold. There is no standard ...
*
Spin foam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structur ...
References
Wayback Machinesee Sec 6.8 Dynamics: III. Group field theory
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Quantum gravity
{{quantum-stub