Abstract
This editorial introduces the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms” which includes a number of research and review articles covering results in the group field theory (GFT) formalism for quantum gravity and in various neighbouring areas of quantum gravity research. We give a brief overview of the basic ideas of the GFT formalism, list some of its connections to other fields, and then summarise all contributions to the Special Issue.
Highlights
Perimeter Institute for Theoretical Physics, 31 Caroline St
The basic idea behind group field theory (GFT) is to extend the framework of random matrix and tensor models, where a sum over triangulations is generated as the perturbative expansion of a theory of matrices or tensors, by including additional group-theoretic data to be interpreted as the discrete parallel transports of a connection formulation for gravity
Spin foam models of immediate interest for loop quantum gravity [7], for which a more detailed understanding in terms of simplicial geometry is available, can be obtained from the expansion of a GFT for a field with four arguments valued in the Lorentz group or SU(2), with additional geometricity conditions imposed on the kinetic or interaction kernels and combinatorially nonlocal interactions of φ5 type [8]
Summary
The basic idea behind GFT is to extend the framework of random matrix and tensor models, where a sum over triangulations is generated as the perturbative expansion of a theory of matrices or tensors, by including additional group-theoretic data to be interpreted as the discrete parallel transports of a connection formulation for gravity. Spin foam models of immediate interest for loop quantum gravity [7], for which a more detailed understanding in terms of simplicial geometry is available, can be obtained from the expansion of a GFT for a field with four arguments valued in the Lorentz group or SU(2), with additional geometricity conditions imposed on the kinetic or interaction kernels and combinatorially nonlocal interactions of φ5 type [8].
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