Built on

S. Weinberg, Ultraviolet divergences in quantum theories of gravitation , General Relativity: An Einstein centenary survey, Eds. Hawking, S.W., Israel, W; Cambridge University Press (1979) 790–831
1979
Earlier work this paper cites.
L. Bombelli, J. Lee, D. Meyer and R. Sorkin, Space-Time as a Causal Set , Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
R. D. Sorkin, Space-time and causal sets , in Proceedings, 7th Latin American International Symposium on General Relativity and Gravitation: Cocoyoc, Mexico, December 2-7, 1990 , 1990
1990
Earlier work this paper cites.
C. Wetterich, Exact evolution equation for the effective potential , Phys.Lett. B301
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Quantum gravity in (2+epsilon)-dimensions , Prog. Theor. Phys. Suppl. 114
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Scaling exponents in quantum gravity near two-dimensions , Nucl. Phys. B393
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Ultraviolet stable fixed point and scaling relations in (2+epsilon)-dimensional quantum gravity , Nucl. Phys. B404
1993
Earlier work this paper cites.
T. R. Morris, The Exact renormalization group and approximate solutions , Int. J. Mod. Phys. A9
1994
Earlier work this paper cites.
T. Aida, Y. Kitazawa, H. Kawai and M. Ninomiya, Conformal invariance and renormalization group in quantum gravity near two-dimensions , Nucl. Phys. B427
1994
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Renormalizability of quantum gravity near two-dimensions , Nucl. Phys. B467
1996
Earlier work this paper cites.
M. Reuter, Nonperturbative evolution equation for quantum gravity , Phys.Rev. D57
1998
Earlier work this paper cites.
S. Falkenberg and S. D. Odintsov, Gauge dependence of the effective average action in Einstein gravity , Int. J. Mod. Phys. A13
1998
Earlier work this paper cites.
D. F. Litim and J. M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges , Phys.Lett. B435
1998
Earlier work this paper cites.
J. Ambjorn and R. Loll, Nonperturbative Lorentzian quantum gravity, causality and topology change , Nucl. Phys. B536
1998
Earlier work this paper cites.
W. Souma, Nontrivial ultraviolet fixed point in quantum gravity , Prog. Theor. Phys. 102
1999
Earlier work this paper cites.
D. F. Litim, Optimized renormalization group flows , Phys.Rev. D64
2001
Earlier work this paper cites.
O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity , Phys.Rev. D65
2002
Earlier work this paper cites.
O. Lauscher and M. Reuter, Is quantum Einstein gravity nonperturbatively renormalizable? , Class. Quant. Grav. 19
2002
Earlier work this paper cites.
M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , Phys. Rev. D65
2002
Earlier work this paper cites.
O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher derivative truncation , Phys. Rev. D66
2002
Earlier work this paper cites.
D. F. Litim and J. M. Pawlowski, Renormalization group flows for gauge theories in axial gauges , JHEP 09
2002
Earlier work this paper cites.
D. F. Litim, Critical exponents from optimized renormalization group flows , Nucl.Phys. B631
2002
Earlier work this paper cites.
R. Percacci and D. Perini, Constraints on matter from asymptotic safety , Phys. Rev. D67
2003
Earlier work this paper cites.
R. Percacci and D. Perini, Asymptotic safety of gravity coupled to matter , Phys. Rev. D68
2003
Earlier work this paper cites.
R. D. Sorkin, Causal sets: Discrete gravity , in Lectures on quantum gravity. Proceedings, School of Quantum Gravity, Valdivia, Chile, January 4-14, 2002 , pp. 305–327, 2003, gr-qc/0309009 , DOI
2003
Earlier work this paper cites.
D. F. Litim, Fixed points of quantum gravity , Phys. Rev. Lett. 92
2004
Earlier work this paper cites.
O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity , JHEP 10
2005
Earlier work this paper cites.
J. Ambjorn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe , Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
M. Reuter and J.-M. Schwindt, A Minimal length from the cutoff modes in asymptotically safe quantum gravity , JHEP 01
2006
Earlier work this paper cites.
M. Niedermaier and M. Reuter, The Asymptotic Safety Scenario in Quantum Gravity , Living Rev.Rel. 9
2006
Earlier work this paper cites.
A. Codello and R. Percacci, Fixed points of higher derivative gravity , Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
J. M. Pawlowski, Aspects of the functional renormalisation group , Annals Phys. 322
2007
Earlier work this paper cites.
J. M. Martín-García, R. Portugal and L. R. U. Manssur, The Invar tensor package , Computer Physics Communications 177
Original
2007
Earlier work this paper cites.
P. F. Machado and F. Saueressig, On the renormalization group flow of f(R)-gravity , Phys.Rev. D77
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, Ultraviolet properties of f(R)-gravity , Int.J.Mod.Phys. A23
Original
2008
Earlier work this paper cites.
J. M. Martín-García, xPerm: fast index canonicalization for tensor computer algebra , Computer Physics Communications 179
Original
2008
Earlier work this paper cites.
J. M. Martín-García, D. Yllanes and R. Portugal, The Invar tensor package: Differential invariants of Riemann , Computer Physics Communications 179
Original
2008
Earlier work this paper cites.
D. Benedetti, P. F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity , Mod. Phys. Lett. A24
Original
2009
Earlier work this paper cites.
E. Manrique and M. Reuter, Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Reuter and H. Weyer, Background Independence and Asymptotic Safety in Conformally Reduced Gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Reuter and H. Weyer, Conformal sector of Quantum Einstein Gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
P. F. Machado and R. Percacci, Conformally reduced quantum gravity revisited , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
D. Brizuela, J. M. Martin-Garcia and G. A. Mena Marugan, xPert: Computer algebra for metric perturbation theory , Gen. Rel. Grav. 41
Original
2009
Earlier work this paper cites.
D. Benedetti and J. Henson, Spectral geometry as a probe of quantum spacetime , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
K. Groh and F. Saueressig, Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity , J. Phys. A43
Original
2010
Earlier work this paper cites.
O. Zanusso, L. Zambelli, G. P. Vacca and R. Percacci, Gravitational corrections to Yukawa systems , Phys. Lett. B689
Original
2010
Earlier work this paper cites.
J.-E. Daum, U. Harst and M. Reuter, Running Gauge Coupling in Asymptotically Safe Quantum Gravity , JHEP 01
Original
2010
Earlier work this paper cites.
G. Narain and R. Percacci, Renormalization Group Flow in Scalar-Tensor Theories. I , Class.Quant.Grav. 27
Original
2010
Earlier work this paper cites.
G. P. Vacca and O. Zanusso, Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
E. Manrique and M. Reuter, Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety , Annals Phys. 325
Original
2010
Earlier work this paper cites.
D. Benedetti, K. Groh, P. F. Machado and F. Saueressig, The Universal RG Machine , JHEP 1106
Original
2011
Earlier work this paper cites.
E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically Safe Lorentzian Gravity , Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.

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2017

Infinite order quantum-gravitational correlations

Knorr, Benjamin

Understand

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced.

Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton).
This is reminiscent of a local potential approximation in O(N)-symmetric field theories.
As a first proof of principle, we derive the flow equation for the "graviton potential" induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation.

Built on

S. Weinberg, Ultraviolet divergences in quantum theories of gravitation , General Relativity: An Einstein centenary survey, Eds. Hawking, S.W., Israel, W; Cambridge University Press (1979) 790–831
1979
Earlier work this paper cites.
L. Bombelli, J. Lee, D. Meyer and R. Sorkin, Space-Time as a Causal Set , Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
R. D. Sorkin, Space-time and causal sets , in Proceedings, 7th Latin American International Symposium on General Relativity and Gravitation: Cocoyoc, Mexico, December 2-7, 1990 , 1990
1990
Earlier work this paper cites.
C. Wetterich, Exact evolution equation for the effective potential , Phys.Lett. B301
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Quantum gravity in (2+epsilon)-dimensions , Prog. Theor. Phys. Suppl. 114
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Scaling exponents in quantum gravity near two-dimensions , Nucl. Phys. B393
1993
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Ultraviolet stable fixed point and scaling relations in (2+epsilon)-dimensional quantum gravity , Nucl. Phys. B404
1993
Earlier work this paper cites.
T. R. Morris, The Exact renormalization group and approximate solutions , Int. J. Mod. Phys. A9
1994
Earlier work this paper cites.
T. Aida, Y. Kitazawa, H. Kawai and M. Ninomiya, Conformal invariance and renormalization group in quantum gravity near two-dimensions , Nucl. Phys. B427
1994
Earlier work this paper cites.
H. Kawai, Y. Kitazawa and M. Ninomiya, Renormalizability of quantum gravity near two-dimensions , Nucl. Phys. B467
1996
Earlier work this paper cites.
M. Reuter, Nonperturbative evolution equation for quantum gravity , Phys.Rev. D57
1998
Earlier work this paper cites.
S. Falkenberg and S. D. Odintsov, Gauge dependence of the effective average action in Einstein gravity , Int. J. Mod. Phys. A13
1998
Earlier work this paper cites.
D. F. Litim and J. M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges , Phys.Lett. B435
1998
Earlier work this paper cites.
J. Ambjorn and R. Loll, Nonperturbative Lorentzian quantum gravity, causality and topology change , Nucl. Phys. B536
1998
Earlier work this paper cites.
W. Souma, Nontrivial ultraviolet fixed point in quantum gravity , Prog. Theor. Phys. 102
1999
Earlier work this paper cites.
D. F. Litim, Optimized renormalization group flows , Phys.Rev. D64
2001
Earlier work this paper cites.
O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity , Phys.Rev. D65
2002
Earlier work this paper cites.
O. Lauscher and M. Reuter, Is quantum Einstein gravity nonperturbatively renormalizable? , Class. Quant. Grav. 19
2002
Earlier work this paper cites.
M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , Phys. Rev. D65
2002
Earlier work this paper cites.
O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher derivative truncation , Phys. Rev. D66
2002
Earlier work this paper cites.
D. F. Litim and J. M. Pawlowski, Renormalization group flows for gauge theories in axial gauges , JHEP 09
2002
Earlier work this paper cites.
D. F. Litim, Critical exponents from optimized renormalization group flows , Nucl.Phys. B631
2002
Earlier work this paper cites.
R. Percacci and D. Perini, Constraints on matter from asymptotic safety , Phys. Rev. D67
2003
Earlier work this paper cites.
R. Percacci and D. Perini, Asymptotic safety of gravity coupled to matter , Phys. Rev. D68
2003
Earlier work this paper cites.
R. D. Sorkin, Causal sets: Discrete gravity , in Lectures on quantum gravity. Proceedings, School of Quantum Gravity, Valdivia, Chile, January 4-14, 2002 , pp. 305–327, 2003, gr-qc/0309009 , DOI
2003
Earlier work this paper cites.
D. F. Litim, Fixed points of quantum gravity , Phys. Rev. Lett. 92
2004
Earlier work this paper cites.
O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity , JHEP 10
2005
Earlier work this paper cites.
J. Ambjorn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe , Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
M. Reuter and J.-M. Schwindt, A Minimal length from the cutoff modes in asymptotically safe quantum gravity , JHEP 01
2006
Earlier work this paper cites.
M. Niedermaier and M. Reuter, The Asymptotic Safety Scenario in Quantum Gravity , Living Rev.Rel. 9
2006
Earlier work this paper cites.
A. Codello and R. Percacci, Fixed points of higher derivative gravity , Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
J. M. Pawlowski, Aspects of the functional renormalisation group , Annals Phys. 322
2007
Earlier work this paper cites.
J. M. Martín-García, R. Portugal and L. R. U. Manssur, The Invar tensor package , Computer Physics Communications 177
Original
2007
Earlier work this paper cites.
P. F. Machado and F. Saueressig, On the renormalization group flow of f(R)-gravity , Phys.Rev. D77
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, Ultraviolet properties of f(R)-gravity , Int.J.Mod.Phys. A23
Original
2008
Earlier work this paper cites.
J. M. Martín-García, xPerm: fast index canonicalization for tensor computer algebra , Computer Physics Communications 179
Original
2008
Earlier work this paper cites.
J. M. Martín-García, D. Yllanes and R. Portugal, The Invar tensor package: Differential invariants of Riemann , Computer Physics Communications 179
Original
2008
Earlier work this paper cites.
D. Benedetti, P. F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity , Mod. Phys. Lett. A24
Original
2009
Earlier work this paper cites.
E. Manrique and M. Reuter, Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Reuter and H. Weyer, Background Independence and Asymptotic Safety in Conformally Reduced Gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
M. Reuter and H. Weyer, Conformal sector of Quantum Einstein Gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
P. F. Machado and R. Percacci, Conformally reduced quantum gravity revisited , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
D. Brizuela, J. M. Martin-Garcia and G. A. Mena Marugan, xPert: Computer algebra for metric perturbation theory , Gen. Rel. Grav. 41
Original
2009
Earlier work this paper cites.
D. Benedetti and J. Henson, Spectral geometry as a probe of quantum spacetime , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
K. Groh and F. Saueressig, Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity , J. Phys. A43
Original
2010
Earlier work this paper cites.
O. Zanusso, L. Zambelli, G. P. Vacca and R. Percacci, Gravitational corrections to Yukawa systems , Phys. Lett. B689
Original
2010
Earlier work this paper cites.
J.-E. Daum, U. Harst and M. Reuter, Running Gauge Coupling in Asymptotically Safe Quantum Gravity , JHEP 01
Original
2010
Earlier work this paper cites.
G. Narain and R. Percacci, Renormalization Group Flow in Scalar-Tensor Theories. I , Class.Quant.Grav. 27
Original
2010
Earlier work this paper cites.
G. P. Vacca and O. Zanusso, Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
E. Manrique and M. Reuter, Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety , Annals Phys. 325
Original
2010
Earlier work this paper cites.
D. Benedetti, K. Groh, P. F. Machado and F. Saueressig, The Universal RG Machine , JHEP 1106
Original
2011
Earlier work this paper cites.
E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically Safe Lorentzian Gravity , Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.