Positivity violation for the lattice Landau gluon propagator

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=80³,140³) 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∈[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.