Related papers: Reconstructing the Vacuum Functional of Yang-Mills…
Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…
For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals, however this does not satisfy the obvious form of the Schr\"odinger equation. For…
The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the…
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of…
The Yang-Mills functional integral is studied in an axial variant of 't Hooft's maximal Abelian gauge. In this gauge Gau\ss ' law can be completely resolved resulting in a description in terms of unconstrained variables. Compared to…
We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum…
In the context of two-dimensional large-$N$ lattice Yang--Mills theory, we perform a refined study of the surface sums defined in the companion work [BCSK24]. In this setting, the surface sums are a priori expected to exhibit significant…
Ratios of the true Yang-Mills vacuum wavefunctional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test…
Working in a Hamiltonian formulation with $A_0 = 0$ gauge and also in a path integral formulation, we show that the vacuum wave functional of four-dimensional pure Yang-Mills theory has the form of the exponential of a {\it…
For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schr\"odinger equation from which the expansion coefficents can be found.…
Inspired by the center-vortex dominance in the infrared sector of $SU(N)$ Yang-Mills theory observed on the lattice, we propose a vacuum wave functional localized on an ensemble of correlated center vortices endowed with stiffness and…
The vacuum energy is calculated for Yang-Mills (YM) system defined in $D$ dimensional space-time of $S^1\times R^d$ ($D=d+1$), where the possibility of the YM fields to acquire the vacuum expectation values on $S^1$ is taken into account.…
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both…
The vacuum expectation value of the Wilson loop functional in pure Yang-Mills theory on an arbitrary two-dimensional orientable manifold is studied. We consider the calculation of this quantity for the abelian theory in the continuum case…
The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in…
The leading short-time behaviour of the Yang-Mills Schroedinger functional is obtained within a local expansion in the fields.
For slowly varying fields the Yang-Mills Schroedinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schroedinger functional for arbitrarily varying fields to be…
We present a very simple and explicit procedure for nonlocalizing the action of any theory which can be formulated perturbatively. When the resulting nonlocal field theory is quantized using the functional formalism --- with unit measure…
In the high temperature phase of Yang-Mills theories, large spatial Wilson loops show area law behaviour with a string tension that grows with increasing temperature. Within the framework of the commonly used string picture we use a large…
One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert…