Geodesic
Excited single-particle states of the transfer matrix of the gauge lattice Yang–Mills field with gauge group $U(1)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 2, pp. 218-222 Cet article a éte moissonné depuis la source Math-Net.Ru

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A gauge model of a Yang–Mills field on the lattice $\mathbb Z^{\nu+1}$ with gauge group $U(1)$ at large values of the coupling constant $g$ is considered. It is proved that there exist $\frac 13\nu(\nu-1) (16\nu-26)$ single-particle pairwise orthogonal subspaces invariant with respect to the gaugeinvariant part of the transfer matrix $\mathcal F^{(i)}$ on which the spectrum of $\mathcal F^{(i)}$ is of order $\beta^6$ ($\beta=2/g^2$). The construction of a description of these subspaces makes it possible to determine the spectrum of the operator $\mathcal F^{(i)}$ on them more accurately. The case $\nu=2$ is studied in detail. 
@article{TMF_1988_74_2_a6,
     author = {E. A. Zhizhina},
     title = {Excited single-particle states of the transfer matrix of the gauge lattice {Yang{\textendash}Mills} field with gauge group $U(1)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {218--222},
     year = {1988},
     volume = {74},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_74_2_a6/}
}
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E. A. Zhizhina. Excited single-particle states of the transfer matrix of the gauge lattice Yang–Mills field with gauge group $U(1)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 2, pp. 218-222. http://geodesic.mathdoc.fr/item/TMF_1988_74_2_a6/

[1] Abdulla-Zade F. G., TMF, 45:2 (1980), 276–279 | MR

[2] Minlos R. A., Khrapov P. V., TMF, 61:3 (1984), 460–465 | MR

[3] Khrapov P. V., Transfer-matritsy gibbsovskikh polei s beskonechnym prostranstvom spinov, Dis. ...kand. fiz.-matem. nauk, MGU, M., 1984

[4] Schor S., Nucl. Phys., B222 (1983), 71–82 | DOI | MR

[5] Schor S., Phys. Lett., B132 (1983), 161–164 | DOI

[6] Minlos R. A., Sinai Ya. G., TMF, 2:2 (1970), 230–243 | MR

[7] Malyshev V. A., Minlos R. A., J. Stat. Phys., 21:3 (1979), 231–242 | DOI | MR

[8] Malyshev V. A., Minlos R. A., Commun. Math. Phys., 82 (1981), 211–226 | DOI | MR | Zbl