Abstract
We investigate spin- and velocity-dependent contributions to the gravitational inter-particle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the non-relativistic gravitational potential associated with the scattering of spin-0 and -1/2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the case of electromagnetic potentials. Moreover, we apply our results to explicit examples of form factors based on non-perturbative approaches for quantum gravity. Finally, the cancellation of Newtonian singularity is analysed in the presence of terms beyond the monopole-monopole sector.
Highlights
The current paradigm in the description of the gravitational interaction has foundation in Einstein’s general relativity (GR), that describes gravity as a classical field theory for the space-time dynamics
In what follows we present our results for the NR gravitational potential, taking into account the scattering of both massive spin-0 and spin-1=2 particles, with quantum corrections being included in terms of general form factors Fð□Þ and Wð□Þ
As a first example we consider form factors motivated by an approach of reconstruction of the effective action for quantum gravity based in data obtained via causal dynamical triangulation (CDT)
Summary
The current paradigm in the description of the gravitational interaction has foundation in Einstein’s general relativity (GR), that describes gravity as a classical field theory for the space-time dynamics. In this work we investigate spin- and velocity-dependent contribution to the gravitational inter-particle potential within a framework motivated by quantum gravity models. Our main goal is to present a detailed discussion on the structure of possible quantum corrections to each sector beyond the monopole-monopole interaction For this purpose, we combine the effective action formalism with an expansion in terms of form factors to introduce quantum corrections at the level of the graviton propagator. We combine the effective action formalism with an expansion in terms of form factors to introduce quantum corrections at the level of the graviton propagator This strategy allows us to explore structural aspects of spin- and velocity-dependent contributions without relying on any specific perturbative calculation. The Riemann and Ricci curvature tensors were defined as Rμναβ 1⁄4 ∂αΓμνβ þ ΓμαλΓλνβ − ðα ↔ βÞ and Rμν 1⁄4 Rαμαν, respectively
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