Fractional Propagators and Noncommutative Deformations-A Unified Framework for Nonlocal Spectral Enhancement

This work studies nonlocal effects in scalar field theories by combining two approaches: fractional kinetic operators and noncommutative geometric deformations. Fractional propagators introduce long-range correlations by redistributing spectral modes in momentum space. Noncommutative geometry, implemented through the Moyal star product, modifies interaction vertices by introducing phase-dependent corrections. At the quantum level, the interaction between these two mechanisms naturally leads to UV/IR mixing phenomena. In particular, the emergence of infrared singularities depends on the relation between the spacetime dimension and the fractional parameter. This framework provides a unified description of spectral and geometric forms of nonlocality in quantum field theory.