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

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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, k(2) / k(4) + (gamma) over cap (4), can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses +/- i (gamma) over cap (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.
Keywords
NONPERTURBATIVE SOLUTION, LANDAU GAUGE, SELF-CONSISTENCY, CRITICAL LIMIT, QCD, INTEGRALS, LATTICE GAUGE-THEORY, EXTENDED ITERATIVE SCHEME, EUCLIDEAN GREENS FUNCTIONS, DYSON-SCHWINGER-EQUATIONS

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Chicago
Baulieu, L, David Dudal, MS Guimaraes, MQ Huber, SP Sorella, Nele Vandersickel, and D Zwanziger. 2010. “Gribov Horizon and I-particles: About a Toy Model and the Construction of Physical Operators.” Physical Review D 82 (2).
APA
Baulieu, L., Dudal, D., Guimaraes, M., Huber, M., Sorella, S., Vandersickel, N., & Zwanziger, D. (2010). Gribov horizon and i-particles: about a toy model and the construction of physical operators. PHYSICAL REVIEW D, 82(2).
Vancouver
1.
Baulieu L, Dudal D, Guimaraes M, Huber M, Sorella S, Vandersickel N, et al. Gribov horizon and i-particles: about a toy model and the construction of physical operators. PHYSICAL REVIEW D. 2010;82(2).
MLA
Baulieu, L, David Dudal, MS Guimaraes, et al. “Gribov Horizon and I-particles: About a Toy Model and the Construction of Physical Operators.” PHYSICAL REVIEW D 82.2 (2010): n. pag. Print.
@article{1579066,
  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, k(2) / k(4) + (gamma) over cap (4), can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses +/- i (gamma) over cap (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.},
  articleno    = {025021},
  author       = {Baulieu, L and Dudal, David and Guimaraes, MS and Huber, MQ and Sorella, SP and Vandersickel, Nele and Zwanziger, D},
  issn         = {1550-7998},
  journal      = {PHYSICAL REVIEW D},
  keyword      = {NONPERTURBATIVE SOLUTION,LANDAU GAUGE,SELF-CONSISTENCY,CRITICAL LIMIT,QCD,INTEGRALS,LATTICE GAUGE-THEORY,EXTENDED ITERATIVE SCHEME,EUCLIDEAN GREENS FUNCTIONS,DYSON-SCHWINGER-EQUATIONS},
  language     = {eng},
  number       = {2},
  pages        = {29},
  title        = {Gribov horizon and i-particles: about a toy model and the construction of physical operators},
  url          = {http://dx.doi.org/10.1103/PhysRevD.82.025021},
  volume       = {82},
  year         = {2010},
}

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