Positivity violation for the lattice Landau gluon propagator

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Cucchieri, Attilio
Mendes, Tereza
Taurines, Andre R. [UNESP]

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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<sup>3</sup>, 140<sup>3</sup>) and for three different lattice couplings in the scaling region (β = 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 ε [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. © 2005 The American Physical Society.



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Physical Review D - Particles, Fields, Gravitation and Cosmology, v. 71, n. 5, p. 1-5, 2005.