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Positivity violation for the lattice Landau gluon propagator

Attilio Cucchieri·Tereza Mendes·Andre R. Taurines
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Abstract

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.

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Attilio Cucchieri, Tereza Mendes, Andre R. Taurines. 2005-03-23. Positivity violation for the lattice Landau gluon propagator. https://doi.org/10.1103/physrevd.71.051902

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