Geodesic
Pauli--Villars regularization for some models with singular perturbations
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 54-70

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We show how Pauli–Villars regularization works in the construction of renormalized Hamiltonian for two examplars of quantum systems with singular pertuabations. The systems are the scalar 3-dimensional particle interacting with $\delta$-potential and the infrared extensions of the quadratic forms of the gaussian functional of the ground state in the quantum field theory. 
@article{ZNSL_2021_509_a3,
     author = {T. A. Bolokhov},
     title = {Pauli--Villars regularization for some models with singular perturbations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {54--70},
     publisher = {mathdoc},
     volume = {509},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a3/}
}
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T. A. Bolokhov. Pauli--Villars regularization for some models with singular perturbations. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 54-70. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a3/