Excited single-particle states of the transfer matrix of the gauge lattice Yang–Mills field with gauge group $U(1)$

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.