Gauge fields and ghosts in Rindler space

We consider a two-dimensional Maxwell system defined on the Rindler space with metric ds(2) = exp(2a xi).(d eta(2) - d xi(2)) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space-time with metric ds(2) = dt(2) - dx(2). This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive-and negative-frequency modes. The corresponding mixture cannot be avoided because the projections to positive-frequency modes with respect to Minkowski time t and positive-frequency modes with respect to the Rindler observer's proper time eta are not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space cannot hold in the Rindler space. In the Becchi-Rouet-Stora-Tyutin (BRST) approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum vertical bar 0 > observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space-time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the ghost condensate when the ghost degrees of freedom cannot propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple two-dimensional model support the claim made in a previous paper [F. R. Urban and A. R. Zhitnitsky, Nucl. Phys. B835, 135 (2010).] that the ghost contribution might be responsible for the observed dark energy in a four-dimensional Friedmann-Lemaitre-Robertson-Walker universe.