Fractional Propagators and Noncommutative Deformations: An Expanded One-Loop Analysis of Nonlocal Spectral Enhancement

This work investigates nonlocal behavior in scalar field theories by combining a fractional kinetic operator with a Moyal-type noncommutative deformation. The free Euclidean theory is characterized by a fractional propagator whose ultraviolet scaling is controlled by the fractional parameter. A quartic Moyal interaction is then introduced, and the one-loop two-point function is derived explicitly, separating the planar and non-planar tadpole contributions and their corresponding combinatorial factors. The non-planar contribution is analyzed by Schwinger parametrization, making explicit the dependence of its leading non-analytic behavior on the spacetime dimension and the fractional parameter. The analysis shows how the infrared singularity at vanishing external momentum originates from the ultraviolet region of the loop integral, providing a fractional generalization of the familiar Moyal-space UV/IR-mixing mechanism.