A Toy Model For Nonlocal Quantum Gravity

Nonlocal quantum gravity is a promising candidate for quantum theory of gravity.In this thesis,a class of nonlocal scalar field theory will be constructed as a toy model of quantum gravity.This class of field theory,under a more genernal framework,has been proved earlier to be unitary.In the thesis,we will first introduce the motivations of constructing a field theory which is nonlocalized as well as the history of nonlocal quantum gravity.As a comparison,we introduce the normal prescription for the localized field theory and the problem for such prescription treating with nonlocalized field theory.We will show you how to transfer the scattering amplitudes from Euclidean space to Minkowski space by means of analytic continuation.As for the calculation of the scattering amplitude,we first compute the one-loop amplitudes for three different nonlocal form factors and the two-loop amplitudes for one of the form factors.Afterward,we compute the scattering amplitudes in Minkowski space with real and positive external energies which is constructed through analytic continuation.Such analytic continuation method will be applied to the one-loop amplitude for two out of three nonlocal form factors.We want to verify the finiteness and unitarity of the nonlocal scalar field theory.