Gauge-invariant master field in U(∞) LGT: A pathway from the strong to weak coupling phases

Path integral for the loop representation of lattice gauge theories

“…Using equation (12) and integrating over θ ℓ we get a δ(δn p ). Then, we arrive to the following functional of the integer 2-forms n…”

“…(31) † The relation between the surfaces of the Wilson action and those of Weingarten action has been analyzed by Kazakov et al in ref. [12].…”

A String Project in Multicolour QCD

“…Then we can solve the resulting equation by standard methods and define the inverse momenta < tr N α −k > (the weights of the "surface") from the self-consistency condition. The "sum over surfaces" with these weights will reproduce the correct result (4.25) for sufficiently big M. This method was checked numerically in [9] on a similar construction and the convergency with M turned out to be very fast.…”

“…To explain the idea of the modified SC expansion, proposed in [4] and tested on some examples in [9], we consider two similar, but technically slightly different approaches.…”

“…We will use a method for its solution explaned in [9] which recalls our first construction. Namely we parametrize the Haar measure in (4.1) by the lagrange multiplier α, as in (3.3), and after the integration over the complex matrix U we obtain the following 1-matrix model:…”