Abstract
We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum. We find an infinite number of poles with positive mass, but both positive and negative effective width, and studied their asymptotic behaviour in the infinite sheet Riemann surface. We find that the stability of these precursors depend crucially on the value of the normalisation point scale.
Highlights
Propagators play a crucial role in both quantum mechanics and in quantum field theory
We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum
The existence of this pole implies the same pole in the effective charge of the electron. The latter can be removed by imposing causality and using some adequate analytic properties of propagators [5,6]. The generalisation of this procedure was later applied to quantum chromodynamics (QCD) [7], resulting in the successful description of various physical processes [8]
Summary
Propagators play a crucial role in both quantum mechanics (see e.g. [1]) and in quantum field theory (see e.g. [2,3]). As is well-known, the appearance of a pole in the free field propagator (p2 = m2) tells us that there exists a one-particle state with the corresponding mass m. The existence of this pole implies the same pole in the effective charge of the electron The latter can be removed by imposing causality and using some adequate analytic properties of propagators [5,6]. The generalisation of this procedure was later applied to quantum chromodynamics (QCD) [7], resulting in the successful description of various physical processes [8]. The resummed one-loop propagator of the graviton interacting with matter fields was obtained [9,10] (see Appendix A). We reveal a multisheet structure of the corresponding Riemann surface, the role of the renormalisation point and some analogies with studies of the propagator in QCD
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