Applications of Integral Equations in Contemporary Physics: A Systematic Review in Electromagnetism, Quantum Mechanics, and Artificial Intelligence
DOI:
https://doi.org/10.63688/cvxarz46Keywords:
integral equations, contemporary physics, electromagnetism, quantum mechanics, artificial intelligenceAbstract
Integral equations constitute a fundamental mathematical tool for modeling and analyzing complex physical phenomena. Their ability to represent nonlocal interactions and spatial-temporal dependencies has enabled their application in several fields of contemporary physics, particularly electromagnetism, quantum mechanics, and scientific computing. The aim of this research was to analyze the main applications of integral equations in contemporary physics through a systematic literature review. The study adopted a qualitative descriptive-analytical approach and followed the PRISMA 2020 guidelines. The literature search was conducted in specialized databases, including Scopus, Web of Science, ScienceDirect, SpringerLink, IEEE Xplore, and Google Scholar, considering publications between 2020 and 2025. After applying inclusion and exclusion criteria, 15 studies were selected for analysis. The results reveal that integral equations play an essential role in solving complex electromagnetic problems, describing quantum systems, and developing advanced computational methods. Furthermore, a growing integration between integral equations and artificial intelligence was identified, particularly through physics-informed neural networks and neural integral equations. It is concluded that these mathematical tools remain indispensable for the advancement of scientific and technological research in contemporary physics.
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Copyright (c) 2026 Wilmer Javier Labre Tarco, Paul Favian Barrionuevo Cazar , Juan José Medina Hernández, Edisson Mauricio Lalaleo Quispe, Alexi Fernando Sharup Puwainchir (Autor/a)
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