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

Abstract

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. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.

35 pages, 10 .pdf figures. v2: version accepted for publication in Physical Review D

References in corpus (7)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• The Physics of Glueballs
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Soft breaking of BRST invariance for introducing non-perturbative infrared effects in a local and renormalizable way
• Gribov horizon and BRST symmetry: a few remarks
• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
• A renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework

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