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 
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/
@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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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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