### Abstract

Restricting the functional integral to the Gribov region Ω 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, k2k4+γ^{^}4, can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses ±iγ ^{^}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.

Original language | English (US) |
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Article number | 025021 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 82 |

Issue number | 2 |

DOIs | |

State | Published - Jul 30 2010 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*82*(2), [025021]. https://doi.org/10.1103/PhysRevD.82.025021

**Gribov horizon and i-particles : About a toy model and the construction of physical operators.** / Baulieu, L.; Dudal, D.; Guimaraes, M. S.; Huber, M. Q.; Sorella, S. P.; Vandersickel, N.; Zwanziger, D.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 82, no. 2, 025021. https://doi.org/10.1103/PhysRevD.82.025021

}

TY - JOUR

T1 - Gribov horizon and i-particles

T2 - About a toy model and the construction of physical operators

AU - Baulieu, L.

AU - Dudal, D.

AU - Guimaraes, M. S.

AU - Huber, M. Q.

AU - Sorella, S. P.

AU - Vandersickel, N.

AU - Zwanziger, D.

PY - 2010/7/30

Y1 - 2010/7/30

N2 - Restricting the functional integral to the Gribov region Ω 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, k2k4+γ^4, can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses ±iγ ^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.

AB - Restricting the functional integral to the Gribov region Ω 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, k2k4+γ^4, can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses ±iγ ^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.

UR - http://www.scopus.com/inward/record.url?scp=77955612083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955612083&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.82.025021

DO - 10.1103/PhysRevD.82.025021

M3 - Article

VL - 82

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 2

M1 - 025021

ER -