Issue |
EPL
Volume 147, Number 2, August 2024
|
|
---|---|---|
Article Number | 22001 | |
Number of page(s) | 7 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ad5eb7 | |
Published online | 21 August 2024 |
The stationary Klein-Gordon equation with a delta-like source: A generalized function approach
Instituto de Física e Química, Universidade Federal de Itajubá - Avenida BPS 1303, Itajubá, 37500-903, MG, Brazil
Received: 28 May 2024
Accepted: 3 July 2024
This work aims to initiate a discussion on finding solutions to non-homogeneous 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 renormalization process in a wide range of theories.
© 2024 EPLA
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