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arXiv · 2508.18329

The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach

J. P. Ferreira·F. E. Barone·F. A. Barone
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Abstract

This work aims to initiate a discussion on finding solutions to non-homoge\-neous differential equations in terms of generalized functions. For simplicity, we conduct the analysis within the specific context of the stationary Klein-Gordon equation with a point-like source, identifying a generalized function that solves such an equation and aligns with the solution obtained through the Fourier approach with dimensional regularization. In addition to being regular at the source singularity, a notable advantage of our solution is its presentation as a single expression, eliminating the need for piecewise definitions. The arguments presented here are applicable to a broader range of situations, offering a novel approach to addressing divergences in field theories using generalized functions. Moreover, we anticipate that the approach introduced in this work could provide a new method for handling Green functions regularized at coincident points, thereby simplifying the renorma\-lization process in a wide range of theories.

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BibTeXRIS

J. P. Ferreira, F. E. Barone, F. A. Barone. 2025-08-25. The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach. https://doi.org/10.1209/0295-5075%2Fad5eb7

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