Gribov horizon and i-particles: about a toy model and the construction of physical operators

Understand

Restricting the functional integral to the Gribov region $\Omega$ leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region.

• For example, a gluon propagator of the Gribov type, $\frac{k^2}{k^4+{\hat \gamma}^4}$, can be viewed as a propagating pair of unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat \gamma}^2$.
• From this viewpoint, gluons are unphysical and one can see them as being confined.
• We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of $i$-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density.