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Colored Group Field Theory [PDF]

Communications in Mathematical Physics, 2009
Group field theories are higher dimensional generalizations of matrix models. Their Feynman graphs are fat and in addition to vertices, edges and faces, they also contain higher dimensional cells, called bubbles.
A. Perez, D. Oriti, D.V. Boulatov, E.R. Livine, F. Conrady, F. David, H. Grosse, J. Ambjorn, J. Ambjorn, J. Ambjorn, J. Engle, J. Engle, J.B. Geloun, J.W. Barrett, L. Freidel, L. Freidel, L. Freidel, M. Disertori, M. Gross, M. Mulazzani, N. Sasakura, R. De Pietri, R. Gurau, R. Williams, Razvan Gurau, V. Bonzom, V.G. Turaev, W.J. Fairbairn   +27 more
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Classical Group Field Theory [PDF]

Journal of Mathematical Physics, 2011
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored) defined over a ...
Joseph Ben Geloun, Okuyama K., Rivasseau V.   +2 more
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Aspects of Group Field Theory [PDF]

AIP Conference Proceedings, 2012
I review the basic ingredients of discretized gravity which motivate the introduction of Group Field Theory. Thus I describe the GFT formulation of some models and conclude with a few remarks on the emergence of noncommutative structures in such models ...
Vitale, Patrizia
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Quantum Group Schr\"{o}dinger Field Theory [PDF]

Modern Physics Letters A, 1993
We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $\Delta x=~(1-q)x$.
Ubriaco, Marcelo R.
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Group Field Theory: An overview [PDF]

International Journal of Theoretical Physics, 2005
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory.
A. Mikovic, A. Okolow, A. Perez, A. Perez, A. Perez, D. Oriti, D. Oriti, D. V. Boulatov, E. Witten, E. Witten, F. Markopoulou, H. Ooguri, J. Ambjorn, J. C. Baez, J. C. Baez, J. W. Barrett, J. W. Barrett, J. W. Barrett, L. Freidel, L. Freidel, L. Freidel, L. Freidel, L. Freidel, L. Freidel, M. P. Reisenberger, M. P. Reisenberger, P. Di Francesco, R. De Pietri, R. De Pietri, R. De Pietri, R. De Pietri, T. Thiemann, V. G. Turaev   +32 more
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EPRL/FK Group Field Theory [PDF]

EPL (Europhysics Letters), 2010
The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model.Comment: 20 pages, 2 ...
Ben Geloun J., Ben Geloun J. Gurau R. Rivasseau V., Freidel L., Gurau R., J. Ben Geloun, Krajewski T. Magnen J. Rivasseau V. Tanasa A. Vitale P., Magnen J., Messiah A., Oriti D., Perelomov A., R. Gurau, V. Rivasseau   +11 more
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Bosonic Colored Group Field Theory [PDF]

The European Physical Journal C, 2009
Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied.
A. Abdesselam, C. Rovelli, D.V. Boulatov, H. Ooguri, J. Ben Geloun, J. Engle, J. Feldman, J. Magnen, Jacques Magnen, Joseph Ben Geloun, L. Freidel, L. Freidel, L. Freidel, L. Freidel, P.T. Matthews, P.T. Matthews, T. Thiemann, V. Rivasseau, V. Rivasseau, V. Rivasseau, Vincent Rivasseau   +20 more
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The Heisenberg group and conformal field theory [PDF]

The Quarterly Journal of Mathematics, 2011
A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the "nonlinear Sigma-model" or "lattice-CFT", is given.
Posthuma, Hessel
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Group field theories [PDF]

Proceedings of 3rd Quantum Gravity and Quantum Geometry School — PoS(QGQGS 2011), 2011
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D.
Krajewski, Thomas
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Group field theory on 2-groups

Physical Review D, 2023
Group field theories are quantum field theories built on groups. They can be seen as a tool to generate topological state-sums or quantum gravity models. For four dimensional manifolds, different arguments have pointed towards 2-groups (such as crossed modules) as the relevant symmetry structure to probe four dimensional topological features.
Florian Girelli, Matteo Laudonio, Adrian Tanasa, Panagiotis Tsimiklis   +3 more
openaire   +2 more sources