×

zbMATH — the first resource for mathematics

One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance. (English) Zbl 1382.83042

MSC:
83C45 Quantization of the gravitational field
53Z05 Applications of differential geometry to physics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
Software:
DLMF
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Burgess, C. P., Quantum gravity in everyday life: general relativity as an effective field theory, Living Rev. Relativ., 7, 5, (2004) · Zbl 1070.83009
[2] Ade, P. A R., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys., 594, A13, (2016)
[3] Ade, P. A R., Planck 2015 results. XVII. Constraints on primordial non-Gaussianity, Astron. Astrophys., 594, A17, (2016)
[4] Ade, P. A R., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys., 594, A20, (2016)
[5] Schwinger, J. S., Sources and gravitons, Phys. Rev., 173, 1264, (1968)
[6] Radkowski, A. F., Some aspects of the source description of gravitation, Ann. Phys., 56, 319, (1970)
[7] Duff, M. J., Quantum corrections to the Schwarzschild solution, Phys. Rev. D, 9, 1837, (1974)
[8] Duff, M. J.; Liu, J. T., Complementarity of the Maldacena and Randall–Sundrum pictures, Phys. Rev. Lett., 85, 2052, (2000) · Zbl 1369.83089
[9] Satz, A.; Mazzitelli, F. D.; Alvarez, E., Vacuum polarization around stars: nonlocal approximation, Phys. Rev. D, 71, (2005)
[10] Park, S.; Woodard, R. P., Solving the effective field equations for the Newtonian potential, Class. Quantum Grav., 27, (2010) · Zbl 1206.83080
[11] Marunovic, A.; Prokopec, T., Time transients in the quantum corrected Newtonian potential induced by a massless nonminimally coupled scalar field, Phys. Rev. D, 83, (2011)
[12] Marunovic, A.; Prokopec, T., Antiscreening in perturbative quantum gravity and resolving the Newtonian singularity, Phys. Rev. D, 87, (2013)
[13] Burns, D.; Pilaftsis, A., Matter quantum corrections to the graviton self-energy and the Newtonian potential, Phys. Rev. D, 91, (2015)
[14] Fröb, M. B., Quantum gravitational corrections for spinning particles, J. High Energy Phys., JHEP10(2016), 051, (2016) · Zbl 1390.83028
[15] Wang, C. L.; Woodard, R. P., One-loop quantum electrodynamic correction to the gravitational potentials on de Sitter spacetime, Phys. Rev. D, 92, (2015)
[16] Park, S.; Prokopec, T.; Woodard, R. P., Quantum scalar corrections to the gravitational potentials on de Sitter background, J. High Energy Phys., JHEP01(2016), 074, (2016) · Zbl 1388.83138
[17] Fröb, M. B.; Verdaguer, E., Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter, J. Cosmol. Astropart. Phys., JCAP03(2016), 015, (2016)
[18] Fröb, M. B.; Verdaguer, E., Quantum corrections for spinning particles in de Sitter, J. Cosmol. Astropart. Phys., JCAP04(2017), 022, (2017)
[19] Khavkine, I., Quantum astrometric observables I: time delay in classical and quantum gravity, Phys. Rev. D, 85, (2012)
[20] Bonga, B.; Khavkine, I., Quantum astrometric observables II: time delay in linearized quantum gravity, Phys. Rev. D, 89, (2014)
[21] Battista, E.; Tartaglia, A.; Esposito, G.; Lucchesi, D.; Ruggiero, M. L.; Valko, P.; Dell’Agnello, S.; Di Fiore, L.; Simo, J.; Grado, A., Quantum time delay in the gravitational field of a rotating mass, Class. Quant. Grav., 34, (2017) · Zbl 1371.83077
[22] Battista, E.; Esposito, G., Restricted three-body problem in effective-field-theory models of gravity, Phys. Rev. D, 89, (2014)
[23] Battista, E.; Dell’Agnello, S.; Esposito, G.; Simo, J.; Battista, E.; Dell’Agnello, S.; Esposito, G.; Simo, J., Quantum effects on Lagrangian points and displaced periodic orbits in the Earth–Moon system, Phys. Rev. D. Phys. Rev. D, 93, (2016)
[24] Borgman, J.; Ford, L. H., The Effects of stress tensor fluctuations upon focusing, Phys. Rev. D, 70, (2004)
[25] Drago, N.; Pinamonti, N., Influence of quantum matter fluctuations on geodesic deviation, J. Phys. A: Math. Theor., 47, (2014) · Zbl 1300.81078
[26] Bjerrum-Bohr, N. E J., Leading quantum gravitational corrections to scalar QED, Phys. Rev. D, 66, (2002)
[27] Donoghue, J. F.; Holstein, B. R.; Garbrecht, B.; Konstandin, T.; Donoghue, J. F.; Holstein, B. R.; Garbrecht, B.; Konstandin, T., Quantum corrections to the Reissner–Nordström and Kerr-Newman metrics, Phys. Lett. B. Phys. Lett. B, 612, 311, (2005) · Zbl 1247.83049
[28] Ford, L. H.; Hertzberg, M. P.; Karouby, J., Quantum gravitational force between polarizable objects, Phys. Rev. Lett., 116, (2016)
[29] Torre, C. G., Gravitational observables and local symmetries, Phys. Rev. D, 48, R2373, (1993)
[30] Giddings, S. B.; Marolf, D.; Hartle, J. B., Observables in effective gravity, Phys. Rev. D, 74, (2006)
[31] Khavkine, I., Local and gauge invariant observables in gravity, Class. Quantum Grav., 32, (2015) · Zbl 1327.83125
[32] Donoghue, J. F., Leading quantum correction to the Newtonian potential, Phys. Rev. Lett., 72, 2996, (1994)
[33] Muzinich, I. J.; Vokos, S., Long range forces in quantum gravity, Phys. Rev. D, 52, 3472, (1995)
[34] Hamber, H. W.; Liu, S., On the quantum corrections to the Newtonian potential, Phys. Lett. B, 357, 51, (1995)
[35] Akhundov, A. A.; Bellucci, S.; Shiekh, A., Gravitational interaction to one loop in effective quantum gravity, Phys. Lett. B, 395, 16, (1997)
[36] Kirilin, G. G.; Khriplovich, I. B.; Kirilin, G. G.; Khriplovich, I. B., Quantum power correction to the Newton law, J. Exp. Theor. Phys.. Zh. Eksp. Teor. Fiz., 95, 1139, (2002)
[37] Khriplovich, I. B.; Kirilin, G. G.; Khriplovich, I. B.; Kirilin, G. G., Quantum long range interactions in general relativity, J. Exp. Theor. Phys.. Zh. Eksp. Teor. Fiz., 125, 1219, (2004) · Zbl 1097.83516
[38] Bjerrum-Bohr, N. E J.; Donoghue, J. F.; Holstein, B. R.; Bjerrum-Bohr, N. E J.; Donoghue, J. F.; Holstein, B. R., Quantum corrections to the Schwarzschild and Kerr metrics, Phys. Rev. D. Phys. Rev. D, 71, (2003)
[39] Bjerrum-Bohr, N. E J.; Donoghue, J. F.; Holstein, B. R.; Bjerrum-Bohr, N. E J.; Donoghue, J. F.; Holstein, B. R., Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev. D. Phys. Rev. D, 71, (2003)
[40] Holstein, B. R.; Ross, A., Spin effects in long range gravitational scattering, (2008)
[41] Ware, J.; Saotome, R.; Akhoury, R., Construction of an asymptotic S matrix for perturbative quantum gravity, J. High Energy Phys., JHEP10(2013), 159, (2013)
[42] Donnelly, W.; Giddings, S. B.; Donnelly, W.; Giddings, S. B., Diffeomorphism-invariant observables and their nonlocal algebra, Phys. Rev. D. Phys. Rev. D, 94, (2016)
[43] Donnelly, W.; Giddings, S. B., Observables, gravitational dressing and obstructions to locality and subsystems, Phys. Rev. D, 94, (2016)
[44] Kibble, T. W B., Coherent soft-photon states and infrared divergences. IV. The scattering operator, Phys. Rev., 175, 1624, (1968)
[45] Kulish, P. P.; Faddeev, L. D.; Kulish, P. P.; Faddeev, L. D., Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys.. Teor. Mat. Fiz., 4, 153, (1970) · Zbl 0197.26201
[46] Steinmann, O., Perturbative QED in terms of Gauge invariant fields, Ann. Phys., 157, 232, (1984)
[47] Bagan, E.; Lavelle, M.; McMullan, D., Charges from dressed matter: construction, Ann. Phys., 282, 471, (2000) · Zbl 0990.81144
[48] Bagan, E.; Lavelle, M.; McMullan, D., Charges from dressed matter: physics and renormalisation, Ann. Phys., 282, 503, (2000) · Zbl 0990.81145
[49] Mitra, I.; Ratabole, R.; Sharatchandra, H. S., Gauge-invariant dressed fermion propagator in massless QED(3), Phys. Lett. B, 636, 68, (2006)
[50] Dirac, P. A M., Gauge invariant formulation of quantum electrodynamics, Can. J. Phys., 33, 650, (1955) · Zbl 0068.22801
[51] Marolf, D., Comments on microcausality, chaos and gravitational observables, Class. Quantum Grav., 32, (2015) · Zbl 1331.83046
[52] Brunetti, R.; Fredenhagen, K.; Rejzner, K., Quantum gravity from the point of view of locally covariant quantum field theory, Commun. Math. Phys., 345, 741, (2016) · Zbl 1346.83001
[53] Géhéniau, J.; Debever, R., Les invariants de courbure de l’espace de Riemann à quatre dimensions, Bull. Acad. R. Belg. Cl. Sci., 42, 114, (1956) · Zbl 0073.16902
[54] Géhéniau, J., Les invariants de courbure des espaces Riemanniens de la relativité, Bull. Acad. R. Belg. Cl. Sci., 42, 252, (1956) · Zbl 0073.16903
[55] Debever, R., Étude géométrique du tenseur de Riemann–Christoffel des espaces de Riemann à quatre dimensions, Bull. Acad. R. Belg. Cl. Sci., 42, 313, (1956) · Zbl 0075.31201
[56] Debever, R., Bull. Acad. R. Belg. Cl. Sci., 42, 608, (1956)
[57] Géhéniau, J.; Debever, R., Les quatorze invariants de courbure de l’espace riemannien à quatre dimensions, Helv. Phys. Acta, 29, 101, (1956) · Zbl 0073.16902
[58] Komar, A., Construction of a complete set of independent observables in the general theory of relativity, Phys. Rev., 111, 1182, (1958) · Zbl 0082.21003
[59] Bergmann, P. G.; Komar, A. B., Poisson brackets between locally defined observables in general relativity, Phys. Rev. Lett., 4, 432, (1960)
[60] Bergmann, P. G., Observables in general relativity, Rev. Mod. Phys., 33, 510, (1961) · Zbl 0098.42501
[61] Tambornino, J., Relational observables in gravity: a review, Sigma, 8, 017, (2012) · Zbl 1242.83047
[62] Brunetti, R.; Fredenhagen, K.; Hack, T-P; Pinamonti, N.; Rejzner, K., Cosmological perturbation theory and quantum gravity, J. High Energy Phys., JHEP08(2016), 032, (2016) · Zbl 1390.83059
[63] Tsamis, N. C.; Woodard, R. P., Physical Green’s functions in quantum gravity, Ann. Phys., 215, 96, (1992)
[64] Modanese, G., Vacuum correlations at geodesic distance in quantum gravity, Riv. Nuovo Cim., 17N8, 1, (1994)
[65] Urakawa, Y.; Tanaka, T., Influence on Observation from IR Divergence during inflation. I, Prog. Theor. Phys., 122, 779, (2009) · Zbl 1180.83114
[66] Urakawa, Y.; Tanaka, T., Influence on observation from IR divergence during inflation: multi field inflation, Prog. Theor. Phys., 122, 1207, (2010) · Zbl 1186.83177
[67] Mandelstam, S., Quantization of the gravitational field, Ann. Phys., 19, 25, (1962) · Zbl 0109.20905
[68] Mandelstam, S., Feynman rules for the gravitational field from the coordinate-independent field-theoretic formalism, Phys. Rev., 175, 1604, (1968)
[69] Teitelboim, C., Gravitation theory in path space, Nucl. Phys. B, 396, 303, (1993)
[70] Woodard, R. P., Invariant formulation of and radiative corrections in quantum gravity, PhD Thesis, (1983)
[71] Hamber, H. W., Invariant correlations in simplicial gravity, Phys. Rev. D, 50, 3932, (1994)
[72] Ambjørn, J.; Anagnostopoulos, K. N., Quantum geometry of 2D gravity coupled to unitary matter, Nucl. Phys. B, 497, 445, (1997)
[73] Modanese, G., On the motion of test particles in a fluctuating gravitational field, J. Math. Phys., 33, 4217, (1992) · Zbl 0769.53043
[74] Gervais, J-L; Neveu, A., The slope of the leading regge trajectory in quantum chromodynamics, Nucl. Phys. B, 163, 189, (1980)
[75] Dotsenko, V. S.; Vergeles, S. N., Renormalizability of phase factors in the Nonabelian gauge theory, Nucl. Phys. B, 169, 527, (1980)
[76] Brandt, R. A.; Neri, F.; Sato, M-A, Renormalization of loop functions for all loops, Phys. Rev. D, 24, 879, (1981)
[77] Blanchet, L.; Damour, T.; Esposito-Farèse, G., Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates, Phys. Rev. D, 69, (2004)
[78] Blanchet, L.; Damour, T.; Esposito-Farèse, G.; Iyer, B. R., Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses, Phys. Rev. D, 71, (2005)
[79] Jaranowski, P.; Schäfer, G., Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian, Phys. Rev. D, 87, (2013)
[80] Bernard, L.; Blanchet, L.; Bohé, A.; Faye, G.; Marsat, S., Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation, Phys. Rev. D, 93, (2016)
[81] Misner, C.; Thorne, K.; Wheeler, J. A., Gravitation, (1973), San Francisco, CA: W H Freeman, San Francisco, CA
[82] Leibbrandt, G., Introduction to the technique of dimensional regularization, Rev. Mod. Phys., 47, 849, (1975)
[83] van Nieuwenhuizen, P., Classical gauge fixing in quantum field theory, Phys. Rev. D, 24, 3315, (1981) · Zbl 1267.81249
[84] Woodard, R. P., The vierbein is irrelevant in perturbation theory, Phys. Lett. B, 148, 440, (1984)
[86] Smirnov, V. A., Evaluating Feynman Integrals, (2004), Berlin: Springer, Berlin · Zbl 1098.81003
[87] Kahya, E. O.; Woodard, R. P., Quantum gravity corrections to the one loop scalar self-mass during inflation, Phys. Rev. D, 76, (2007)
[88] Boran, S.; Kahya, E. O.; Park, S., Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background, Phys. Rev. D, 90, (2014)
[89] Boran, S.; Kahya, E. O.; Park, S., Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background. II. Kinetic conformal cross terms, Phys. Rev. D, 96, (2017)
[90] Stefanis, N. G., Connector-korrigierte Quark-Zwei-Punkt-Greens-Funktion in der Ein-Schleifenapproximation, PhD Thesis, (1983)
[91] Stefanis, N. G., Gauge-invariant quark two-point Greens function through connector insertion to \(O(α_s)\), Nuovo Cim. A, 83, 205, (1984)
[92] Giddings, S. B.; Sloth, M. S., Semiclassical relations and IR effects in de Sitter and slow-roll space-times, J. Cosmol. Astropart. Phys., JCAP01(2011), 023, (2011)
[93] Urakawa, Y.; Tanaka, T., IR divergence does not affect the gauge-invariant curvature perturbation, Phys. Rev. D, 82, (2010)
[94] Gerstenlauer, M.; Hebecker, A.; Tasinato, G., Inflationary correlation functions without infrared divergences, J. Cosmol. Astropart. Phys., JCAP06(2011), 021, (2011)
[95] Becchi, C.; Rouet, A.; Stora, R., Renormalization of Gauge Theories, Ann. Phys., 98, 287, (1976)
[96] Batalin, I.; Vilkovisky, G., Gauge algebra and quantization, Phys. Lett. B, 102, 27, (1981)
[97] Batalin, I.; Vilkovisky, G., Quantization of Gauge theories with linearly dependent generators, Phys. Rev. D, 28, 2567, (1983)
[98] Batalin, I.; Vilkovisky, G., Quantization of Gauge theories with linearly dependent generators, Phys. Rev. D, 30, 508, (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.