Group field theory is a theory of quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

. It is closely related to background independent quantum gravity approaches such as loop quantum gravity

Loop quantum gravity

Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

 and spin foam

Spin foam

In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral description of quantum gravity...

 and causal dynamical triangulation.

A group field theory is, technically speaking, a quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

 living on a Lie group

Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...

, whose Feynman diagrams correspond to spin foam

Spin foam

In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral description of quantum gravity...

s and simplicial manifold

Simplicial manifold

In mathematics, the term simplicial manifold commonly refers to either of two different types of objects, which combine attributes of a simplex with those of a manifold. Briefly; a simplex is a generalization of the concept of a triangle into forms with more, or fewer, than two dimensions. ...

s (depending on the representation of the fields). Thus, its partition function

Partition function (quantum field theory)

In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral:...

 defines a non-perturbative sum over all simplicial topologies and geometries, giving a path integral formulation of quantum spacetime

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...

.

See also

• Causal Sets
  Causal sets
  The causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order...
  
  
• Fractal cosmology
  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. More generally, it relates to the usage or appearance of fractals in the study of the universe and...
  
  
• Loop quantum gravity
  Loop quantum gravity
  Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
  
  
• Planck scale
  Planck scale
  In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
  
  
• Quantum gravity
  Quantum gravity
  Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
  
  
• Regge calculus
  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 the early 1960s....
  
  
• Simplex
  Simplex
  In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
  
  
• Simplicial manifold
  Simplicial manifold
  In mathematics, the term simplicial manifold commonly refers to either of two different types of objects, which combine attributes of a simplex with those of a manifold. Briefly; a simplex is a generalization of the concept of a triangle into forms with more, or fewer, than two dimensions. ...
  
  
• Spin foam
  Spin foam
  In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral description of quantum gravity...