One-loop quantum gravity from a worldline viewpoint

• Published in: The journal of high energy physics Vol. 2013; no. 7; pp. 1 - 23
• Main Authors: Bastianelli, Fiorenzo, Bonezzi, Roberto
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2013; Springer Nature B.V
• Subjects: Approximation; Classical and Quantum Gravitation; Cosmological constant; Descriptions; Elementary Particles; High energy physics; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Relativity Theory; Representations; String Theory; Gauge Symmetry; Sigma Models; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2013)016

A
bstract
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.