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Colored Tensor Models - a Review
Colored tensor models have recently burst onto the scene as a promising con- ceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We
Phase space descriptions for simplicial 4D geometries
Starting from the canonical phase space for discretised (4d) BF–theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our
Group field theories for all loop quantum gravity
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional
The shift and commutativity
  • J. Ryan
  • Mathematics
    Mathematical systems theory
  • 1 March 1972
TLDR
It is shown that if Y is the 2-torus and if T is an ergodic group automorphism of Y then the center of the group ~¢(Y, T) of T-commuting homeomorphisms of Y is not ~ (T) and, in fact, that any continuous, onto transformation of X(50) which commutes with all elements of d ( 5 0 ) is a power of 0r.
Melons are Branched Polymers
Melonic graphs constitute the family of graphs arising at leading order in the 1/N expansion of tensor models. They were shown to lead to a continuum phase, reminiscent of branched polymers. We show
Generalized quantum gravity condensates for homogeneous geometries and cosmology
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas
Simplicity in simplicial phase space
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints
TENSOR MODELS AND EMBEDDED RIEMANN SURFACES
Tensor models and, more generally, group field theories are candidates for higher-dimensional quantum gravity, just as matrix models are in the 2D setting. With the recent advent of a $1/N$ expansion
Spin Foam Models with Finite Groups
Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum
The shift and commutivity II
  • J. Ryan
  • Mathematics, Computer Science
    Mathematical systems theory
  • 1 September 1974
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