Interpolating between the Bose-Einstein and the Fermi-Dirac distributions in odd dimensions

We consider the response of a uniformly accelerated monopole detector that is coupled to a superposition of an odd and an even power of a quantized, massless scalar field in flat spacetime in arbitrary dimensions. We show that, when the field is assumed to be in the Minkowski vacuum, the response of the detector is characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response when the dimension of spacetime is odd. Moreover, we find that, it is possible to interpolate between the Bose-Einstein and the Fermi-Dirac distributions in odd spacetime dimensions by suitably adjusting the relative strengths of the detector's coupling to the odd and the even powers of the scalar field. We point out that the response of the detector is always thermal and we, finally, close by stressing the apparent nature of the appearance of the Fermi-Dirac factor in the detector response.Comment: RevTeX, 7 page

Earliest detection of the optical afterglow of GRB 030329 and its variability

We report the earliest detection of an extremely bright optical afterglow of the gamma-ray burst (GRB) 030329 using a 30cm-telescope at Tokyo Institute of Technology (Tokyo, JAPAN). Our observation started 67 minutes after the burst, and continued for succeeding two nights until the afterglow faded below the sensitivity limit of the telescope (approximately 18 mag). Combining our data with those reported in GCN Circulars, we find that the early afterglow light curve of the first half day is described by a broken power-law (t^{- alpha}) function with indices alpha_{1} = 0.88 +/- 0.01 (0.047 < t < t_{b1} days), alpha_{2} = 1.18 +/- 0.01 (t_{b1} < t < t_{b2} days), and alpha_{3} = 1.81 +/- 0.04 (t_{b2} < t < 1.2 days), where t_{b1} ~ 0.26 days and t_{b2} ~ 0.54 days, respectively. The change of the power-law index at the first break at t ~ 0.26 days is consistent with that expected from a ``cooling-break'' when the cooling frequency crossed the optical band. If the interpretation is correct, the decay index before the cooling-break implies a uniform ISM environment.Comment: 13 pages, 1 table and 2 figures. Accepted to the Astrophysical Journal Letter