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We consider the pure Yang-Mills relativistic quantum field theory in animaginary time functional integral formulation. The gauge group is taken to be$\mathcal G = \mathrm U(N)$. We use a lattice ultraviolet regularization,starting with the model defined on a finite hypercubic lattice $\Lambda\subseta\mathbb Z^d$, $d = 2,3,4$, with lattice spacing $a\in (0,1]$ and $L\in\mathbbN$ sites on a side. The Wilson partition function is used where the action is asum over four lattice bond variables of gauge-invariant plaquette (latticeminimal squares) actions with a prefactor $a^{d-4}/g^2$, where we take thegauge coupling $g\in(0,g_0^2]$, $0<g_0<\infty$. In a recent paper, for freeboundary conditions, we proved that a normalized model partition functionsatisfies thermodynamic and ultraviolet stable stability bounds. Here, weextend the stability bounds to the Yang-Mills model with periodic boundaryconditions, with constants which are also independent of $L$, $a$, $g$.Furthermore, we also consider a normalized generating functional for thecorrelations of $r\in\mathbb N$ gauge-invariant plaquette fields. Usingperiodic boundary conditions and the multireflection method, we then prove thatthis generating functional is bounded, with a bound that is independent of $L$,$a$, $g$ and the location and orientation of the $r$ plaquette fields. Thebounds factorize and each factor is a single-bond variable, single-plaquettepartition function. The number of factors is, up to boundary corrections, thenumber of non-temporal lattice bonds, such as $(d-1)L^d$. A new globalquadratic upper bound in the gluon fields is proved for the Wilson plaquetteaction.

On Yang-Mills Stability and Plaquette Field Generating Functional