Built on

B. Dittrich, “Partial and complete observables for Hamiltonian constrained systems”, Gen. Rel. Grav
1927
Earlier work this paper cites.
S. Alexandrov, M. Geiller, and K. Noui, “Spin Foams and Canonical Quantization”, SIGMA
Original
1961
Earlier work this paper cites.
E. Noether, “Invariant variation problems”, Transport Theory and Statistical Physics
1971
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W. Fushchich and V. V. Kornyak, “Computer algebra application for determining lie and lie-bäcklund symmetries of differential equations”, Journal of Symbolic Computation
1989
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M. Gross, “Tensor models and simplicial quantum gravity in > 2-D”, Nucl. Phys. Proc. Suppl
1992
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D. V. Boulatov, “A Model of three-dimensional lattice gravity”, Mod. Phys. Lett
1992
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J. C. Baez, “Spin foam models”, Class. Quant. Grav
1998
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J. W. Barrett and L. Crane, “Relativistic spin networks and quantum gravity”, J. Math. Phys
1998
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L. Freidel, K. Krasnov, and R. Puzio, “BF description of higher dimensional gravity theories”, Adv. Theor. Math. Phys
1999
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P. J. Olver, “Applications of lie groups to differential equations”, Springer Science & Business Media, 2000
2000
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Z. J. Zawistowski, “Symmetries of Integro-Differential Equations”, eConf
2001
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N. H. Ibragimov, V. Kovalev, and V. Pustovalov, “Symmetries of integro-differential equations: A survey of methods illustrated by the benny equations”, Nonlinear Dynamics
2002
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B. Dittrich, “Partial and complete observables for canonical general relativity”, Class. Quant. Grav
2006
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C. Rovelli, “Loop quantum gravity”, Living Reviews in Relativity
2008
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D. Oriti, “The Group field theory approach to quantum gravity: Some recent results”, AIP Conf. Proc
Original
2009
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S. V. Meleshko, Y. N. Grigoriev, N. K. Ibragimov, and V. F. Kovalev, “Symmetries of integro-differential equations: with applications in mechanics and plasma physics”, Springer Science & Business Media, 2010
2010
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A. Baratin and D. Oriti, “Group field theory with non-commutative metric variables”, Phys. Rev. Lett
Original
2010
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J. Ben Geloun, R. Gurau, and V. Rivasseau, “EPRL/FK Group Field Theory”, Europhys. Lett
Original
2010
Earlier work this paper cites.

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2016

Continuous point symmetries in Group Field Theories

Kegeles, Alexander, Oriti, Daniele

Understand

We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective.

We then focus on Group Field Theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.

Built on

B. Dittrich, “Partial and complete observables for Hamiltonian constrained systems”, Gen. Rel. Grav
1927
Earlier work this paper cites.
S. Alexandrov, M. Geiller, and K. Noui, “Spin Foams and Canonical Quantization”, SIGMA
Original
1961
Earlier work this paper cites.
E. Noether, “Invariant variation problems”, Transport Theory and Statistical Physics
1971
Earlier work this paper cites.
W. Fushchich and V. V. Kornyak, “Computer algebra application for determining lie and lie-bäcklund symmetries of differential equations”, Journal of Symbolic Computation
1989
Earlier work this paper cites.
M. Gross, “Tensor models and simplicial quantum gravity in > 2-D”, Nucl. Phys. Proc. Suppl
1992
Earlier work this paper cites.
D. V. Boulatov, “A Model of three-dimensional lattice gravity”, Mod. Phys. Lett
1992
Earlier work this paper cites.
J. C. Baez, “Spin foam models”, Class. Quant. Grav
1998
Earlier work this paper cites.
J. W. Barrett and L. Crane, “Relativistic spin networks and quantum gravity”, J. Math. Phys
1998
Earlier work this paper cites.
L. Freidel, K. Krasnov, and R. Puzio, “BF description of higher dimensional gravity theories”, Adv. Theor. Math. Phys
1999
Earlier work this paper cites.
P. J. Olver, “Applications of lie groups to differential equations”, Springer Science & Business Media, 2000
2000
Earlier work this paper cites.
Z. J. Zawistowski, “Symmetries of Integro-Differential Equations”, eConf
2001
Earlier work this paper cites.
N. H. Ibragimov, V. Kovalev, and V. Pustovalov, “Symmetries of integro-differential equations: A survey of methods illustrated by the benny equations”, Nonlinear Dynamics
2002
Earlier work this paper cites.
B. Dittrich, “Partial and complete observables for canonical general relativity”, Class. Quant. Grav
2006
Earlier work this paper cites.
C. Rovelli, “Loop quantum gravity”, Living Reviews in Relativity
2008
Earlier work this paper cites.
D. Oriti, “The Group field theory approach to quantum gravity: Some recent results”, AIP Conf. Proc
Original
2009
Earlier work this paper cites.
S. V. Meleshko, Y. N. Grigoriev, N. K. Ibragimov, and V. F. Kovalev, “Symmetries of integro-differential equations: with applications in mechanics and plasma physics”, Springer Science & Business Media, 2010
2010
Earlier work this paper cites.
A. Baratin and D. Oriti, “Group field theory with non-commutative metric variables”, Phys. Rev. Lett
Original
2010
Earlier work this paper cites.
J. Ben Geloun, R. Gurau, and V. Rivasseau, “EPRL/FK Group Field Theory”, Europhys. Lett
Original
2010
Earlier work this paper cites.