A Unified View of Physical Regularization: A Proper-Time Filter Function Approach

This paper unifies physical regularization schemes in quantum field theory by introducing a filter function, g(τ), into the Schwinger proper-time integral to tame ultraviolet divergences. We demonstrate that distinct physical postulates for modifying Planck-scale physics correspond to specific mathematical choices for g(τ). A direct connection is established between the analyticity of the filter function and the locality of the resulting field theory: non-analytic filters lead to non-local, ghost-free theories, while analytic filters produce local, higher-derivative theories. This provides a powerful framework for classifying and constructing physically motivated QFTs.