Built on

G. Ponzano and T. Regge, “Semiclassical limit of racah coefficients,” in Spectroscopy and group theoretical methods in physics
1968
Earlier work this paper cites.
K. Wilson, “Confinement of quarks,” Phys. Rev. D 10
1974
Earlier work this paper cites.
B. Dittrich and P. A. Hoehn, “Canonical simplicial gravity,” arXiv:1108.1974 [gr-qc]
Original
1974
Earlier work this paper cites.
K. G. Wilson and J. B. Kogut, “The Renormalization group and the epsilon expansion,” Phys. Rept. 12
1975
Earlier work this paper cites.
C. Rovelli, “Graviton propagator from background-independent quantum gravity,” Phys. Rev. Lett. 97
Original
1978
Earlier work this paper cites.
M. Rocek and R. M. Williams, “Quantum Regge Calculus,” Phys. Lett. B 104
1984
Earlier work this paper cites.
V. G. Turaev., O. ,Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31
1992
Earlier work this paper cites.
W. Bietenholz, “Perfect scalars on the lattice,” Int. J. Mod. Phys. A 15
1996
Earlier work this paper cites.
R. Loll, “Discrete Approaches to Quantum Gravity in Four Dimensions,” Living Reviews in Relativity 13 (1998) online article: [http://relativity.livingreviews.org/Articles/lrr-1998-13/]
1998
Earlier work this paper cites.

Similar

P. Hasenfratz and F. Niedermayer, “Perfect Lattice Action For Asymptotically Free Theories,” Nucl. Phys. B 414
1998
Cited alongside, same era.
A. Ashtekar, C. Rovelli and L. Smolin, “Weaving a classical geometry with quantum threads,” Phys. Rev. Lett. 69
Original
1998
Cited alongside, same era.
T. Regge, “General relativity without coordinates,” Nuovo Cim. 19
2000
Cited alongside, same era.
J. Marsden and M. West “Discrete mechanics and variational integrators” Acta Numerica 10
2001
Cited alongside, same era.
L. Freidel and D. Louapre, “Diffeomorphisms and spin foam models,” Nucl. Phys. B 662
2003
Cited alongside, same era.
“Coarse graining in spin foam models,” Class. Quant. Grav. 20

Then

B. Dittrich, L. Freidel and S. Speziale, “Linearized dynamics from the 4-simplex Regge action,” Phys. Rev. D 76
Original
2007
Later among the works it cites.
B. Bahr and B. Dittrich, “(Broken) Gauge Symmetries and Constraints in Regge Calculus,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
B. Bahr and B. Dittrich, “Improved and Perfect Actions in Discrete Gravity,” Phys. Rev. D 80
Original
2009
Later among the works it cites.
B. Dittrich, “Diffeomorphism symmetry in quantum gravity models,” Adv. Sci. Lett. 2
Original
2009
Later among the works it cites.
R. Gambini and J. Pullin, “Emergent diffeomorphism invariance in a discrete loop quantum gravity model,” Class. Quant. Grav. 26

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2012

How to construct diffeomorphism symmetry on the lattice

Dittrich, Bianca

Understand

Diffeomorphism symmetry, the fundamental invariance of general relativity, is generically broken under discretization.

After discussing the meaning and implications of diffeomorphism symmetry in the discrete, in particular for the continuum limit, we introduce a perturbative framework to construct discretizations with an exact notion of diffeomorphism symmetry.
We will see that for such a perturbative framework consistency conditions need to be satisfied which enforce the preservation of the gauge symmetry to the perturbative order under discussion.
These consistency conditions will allow structural investigations of diffeomorphism invariant discretizations.

Built on

G. Ponzano and T. Regge, “Semiclassical limit of racah coefficients,” in Spectroscopy and group theoretical methods in physics
1968
Earlier work this paper cites.
K. Wilson, “Confinement of quarks,” Phys. Rev. D 10
1974
Earlier work this paper cites.
B. Dittrich and P. A. Hoehn, “Canonical simplicial gravity,” arXiv:1108.1974 [gr-qc]
Original
1974
Earlier work this paper cites.
K. G. Wilson and J. B. Kogut, “The Renormalization group and the epsilon expansion,” Phys. Rept. 12
1975
Earlier work this paper cites.
C. Rovelli, “Graviton propagator from background-independent quantum gravity,” Phys. Rev. Lett. 97
Original
1978
Earlier work this paper cites.
M. Rocek and R. M. Williams, “Quantum Regge Calculus,” Phys. Lett. B 104
1984
Earlier work this paper cites.
V. G. Turaev., O. ,Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31
1992
Earlier work this paper cites.
W. Bietenholz, “Perfect scalars on the lattice,” Int. J. Mod. Phys. A 15
1996
Earlier work this paper cites.
R. Loll, “Discrete Approaches to Quantum Gravity in Four Dimensions,” Living Reviews in Relativity 13 (1998) online article: [http://relativity.livingreviews.org/Articles/lrr-1998-13/]
1998
Earlier work this paper cites.

Similar

P. Hasenfratz and F. Niedermayer, “Perfect Lattice Action For Asymptotically Free Theories,” Nucl. Phys. B 414
1998
Cited alongside, same era.
A. Ashtekar, C. Rovelli and L. Smolin, “Weaving a classical geometry with quantum threads,” Phys. Rev. Lett. 69
Original
1998
Cited alongside, same era.
T. Regge, “General relativity without coordinates,” Nuovo Cim. 19
2000
Cited alongside, same era.
J. Marsden and M. West “Discrete mechanics and variational integrators” Acta Numerica 10
2001
Cited alongside, same era.
L. Freidel and D. Louapre, “Diffeomorphisms and spin foam models,” Nucl. Phys. B 662
2003
Cited alongside, same era.
“Coarse graining in spin foam models,” Class. Quant. Grav. 20

Then

B. Dittrich, L. Freidel and S. Speziale, “Linearized dynamics from the 4-simplex Regge action,” Phys. Rev. D 76
Original
2007
Later among the works it cites.
B. Bahr and B. Dittrich, “(Broken) Gauge Symmetries and Constraints in Regge Calculus,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
B. Bahr and B. Dittrich, “Improved and Perfect Actions in Discrete Gravity,” Phys. Rev. D 80
Original
2009
Later among the works it cites.
B. Dittrich, “Diffeomorphism symmetry in quantum gravity models,” Adv. Sci. Lett. 2
Original
2009
Later among the works it cites.
R. Gambini and J. Pullin, “Emergent diffeomorphism invariance in a discrete loop quantum gravity model,” Class. Quant. Grav. 26

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2003

Cited alongside, same era.

C. Rovelli, “Quantum Gravity” (Cambridge University Press, Cambridge 2004). A. Perez, “The spin foam approach to quantum gravity”, to appear

2004

Cited alongside, same era.

M. Campiglia, C. Di Bartolo, R. Gambini and J. Pullin, “Uniform discretizations: A quantization procedure for totally constrained systems including gravity,” J. Phys. Conf. Ser. 67

2006

Cited alongside, same era.

T. Thiemann, “The Phoenix project: Master constraint program for loop quantum gravity,” Class. Quant. Grav. 23

2006

Cited alongside, same era.

B. Bahr and B. Dittrich, “Breaking and restoring of diffeomorphism symmetry in discrete gravity,” AIP Conference Proceedings Volume 1196, pp. 10-17, [arXiv:0909.5688 [gr-qc]]

Original

Cited in the paper.

C. Rovelli, “Discretizing parametrized systems: the magic of Ditt-invariance,” arXiv:1107.2310 [hep-lat]. C. Rovelli, “On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit,” arXiv:1108.0832 [gr-qc]

Original

Cited in the paper.

B. Bahr, R. Gambini and J. Pullin, “Discretisations, constraints and diffeomorphisms in quantum gravity,” arXiv:1111.1879 [gr-qc]