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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18329 |
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| _version_ | 1866916917495726080 |
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| author | Ferreira, J. P. Barone, F. E. Barone, F. A. |
| author_facet | Ferreira, J. P. Barone, F. E. Barone, F. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach Ferreira, J. P. Barone, F. E. Barone, F. A. Mathematical Physics High Energy Physics - Theory 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. |
| title | The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.18329 |