Abstract
We develop a worldline approach to quantum gravity in D = 4. Using the background field method we consider the covariantly gauge fixed Einstein-Hilbert action with cosmological constant, and find a worldline representation of the differential operators identified by its quadratic approximation. We test it by computing the correct one-loop divergencies. Alternative worldline methods, such as the use of the O(4) spinning particle that is known to describe correctly the propagation of a massless spin 2 particle in D = 4, find obstructions in the coupling to an arbitrary background metric, apparently preventing a more extensive use in perturbative descriptions of quantum gravity. We expect that our model might simplify calculations of one-loop amplitudes with respect to standard quantum field theoretical methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rept. 355 (2001) 73 [hep-th/0101036] [INSPIRE]. arXiv:1304.7135
F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background, Nucl. Phys. B 642 (2002) 372 [hep-th/0205182] [INSPIRE].
F. Bastianelli, O. Corradini and A. Zirotti, dimensional regularization for N = 1 supersymmetric σ-models and the worldline formalism, Phys. Rev. D 67 (2003) 104009 [hep-th/0211134] [INSPIRE].
F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields, JHEP 04 (2005) 010 [hep-th/0503155] [INSPIRE].
F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields. II, JHEP 10 (2005) 114 [hep-th/0510010] [INSPIRE].
F. Bastianelli and C. Schubert, One loop photon-graviton mixing in an electromagnetic field. Part 1, JHEP 02 (2005) 069 [gr-qc/0412095] [INSPIRE].
V. Gershun and V. Tkach, classical and quantum dynamics of particles with arbitrary spin, JETP Lett. 29 (1979) 288 [Pisma Zh. Eksp. Teor. Fiz. 29 (1979) 320] [INSPIRE].
P.S. Howe, S. Penati, M. Pernici and P.K. Townsend, A particle mechanics description of antisymmetric tensor fields, Class. Quant. Grav. 6 (1989) 1125 [INSPIRE].
S. Kuzenko and Z. Yarevskaya, Conformal invariance, N extended supersymmetry and massless spinning particles in anti-de Sitter space, Mod. Phys. Lett. A 11 (1996) 1653 [hep-th/9512115] [INSPIRE].
F. Bastianelli, O. Corradini and E. Latini, Spinning particles and higher spin fields on (A)dS backgrounds, JHEP 11 (2008) 054 [arXiv:0810.0188] [INSPIRE].
P. Dai, Y.-t. Huang and W. Siegel, Worldgraph Approach to Yang-Mills amplitudes from N =2 Spinning Particle, JHEP 10(2008) 027 [arXiv:0807.0391][INSPIRE].
G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69 [INSPIRE].
S. Christensen and M. Duff, Quantizing gravity with a cosmological constant, Nucl. Phys. B 170 (1980) 480 [INSPIRE].
G. de Berredo-Peixoto, A. Penna-Firme and I.L. Shapiro, One loop divergences of quantum gravity using conformal parametrization, Mod. Phys. Lett. A 15 (2000) 2335 [gr-qc/0103043] [INSPIRE].
F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, Effective action for higher spin fields on (A)dS backgrounds, JHEP 12 (2012) 113 [arXiv:1210.4649] [INSPIRE].
M. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179 [INSPIRE].
G. Gibbons, S. Hawking and M. Perry, Path integrals and the indefiniteness of the gravitational action, Nucl. Phys. B 138 (1978) 141 [INSPIRE].
P.O. Mazur and E. Mottola, The gravitational measure, solution of the conformal factor problem and stability of the ground state of quantum gravity, Nucl. Phys. B 341 (1990) 187 [INSPIRE].
H. Kleinert and A. Chervyakov, Reparametrization invariance of path integrals, Phys. Lett. B 464 (1999) 257 [hep-th/9906156] [INSPIRE].
F. Bastianelli, O. Corradini and P. van Nieuwenhuizen, Dimensional regularization of the path integral in curved space on an infinite time interval, Phys. Lett. B 490 (2000) 154 [hep-th/0007105] [INSPIRE].
F. Bastianelli, O. Corradini and P. van Nieuwenhuizen, Dimensional regularization of nonlinear σ-models on a finite time interval, Phys. Lett. B 494 (2000) 161 [hep-th/0008045] [INSPIRE].
F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, Extended SUSY quantum mechanics: transition amplitudes and path integrals, JHEP 06 (2011) 023 [arXiv:1103.3993] [INSPIRE].
F. Bastianelli, The path integral for a particle in curved spaces and Weyl anomalies, Nucl. Phys. B 376 (1992) 113 [hep-th/9112035] [INSPIRE].
F. Bastianelli and P. van Nieuwenhuizen, Trace anomalies from quantum mechanics, Nucl. Phys. B 389 (1993) 53 [hep-th/9208059] [INSPIRE].
U. Muller, C. Schubert and A.M. van de Ven, A closed formula for the Riemann normal coordinate expansion, Gen. Rel. Grav. 31 (1999) 1759 [gr-qc/9712092] [INSPIRE].
F. Bastianelli and O. Corradini, 6 − D trace anomalies from quantum mechanical path integrals, Phys. Rev. D 63 (2001) 065005 [hep-th/0010118] [INSPIRE].
F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press, Cambridge U.K. (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1304.7135
Rights and permissions
About this article
Cite this article
Bastianelli, F., Bonezzi, R. One-loop quantum gravity from a worldline viewpoint. J. High Energ. Phys. 2013, 16 (2013). https://doi.org/10.1007/JHEP07(2013)016
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2013)016