Geodesic
Applicability condition of a cutoff in two-dimensional models
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 153-168

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The paper discusses a condition of applicability for a cutoff regularization in the coordinate representation in two-dimensional Euclidean space. Several important properties and examples are presented. Specifically, it is shown that the set of functions satisfying the condition is non-empty. Furthermore, a more stringent formulation of the condition is possible. Using the example of a two-loop quantum correction for a two-dimensional non-linear sigma model, the application of the cutoff regularization is demonstrated. 
@article{ZNSL_2024_532_a7,
     author = {A. V. Ivanov},
     title = {Applicability condition of a cutoff in two-dimensional models},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {153--168},
     publisher = {mathdoc},
     volume = {532},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a7/}
}
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A. V. Ivanov. Applicability condition of a cutoff in two-dimensional models. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 153-168. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a7/