Geodesic
Exactly solvable quantum mechanical models with Stückelberg divergences
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 1, pp. 91-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue of the model of $N$ scalar fields $(\lambda/N)(\varphi^a\varphi^a)^2$ in the leading order in $1/N$. The model involves vacuum and $S$-matrix divergences and also the Stückelberg divergences, which are absent in other known renormalizable quantum mechanical models with divergences (such as the particle in a $\delta$-shape potential or the Lee model). To eliminate divergences, we renormalize the vacuum energy and charge and transform the Hamiltonian by a unitary transformation with a singular dependence on the regularization parameter. We construct the Hilbert space with a positive-definite metric, a self-adjoint Hamiltonian operator, and a representation for the operators of physical quantities. Neglecting the terms that lead to the vacuum divergences fails to improve and, on the contrary, worsens the renormalizability properties of the model. 
@article{TMF_2000_125_1_a3,
     author = {O. Yu. Shvedov},
     title = {Exactly solvable quantum mechanical models with {St\"uckelberg} divergences},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {91--106},
     year = {2000},
     volume = {125},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_125_1_a3/}
}
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O. Yu. Shvedov. Exactly solvable quantum mechanical models with Stückelberg divergences. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 1, pp. 91-106. http://geodesic.mathdoc.fr/item/TMF_2000_125_1_a3/

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