Alladi Ramakrishnan Hall

Green's function of the Vector fields on DeSitter Background

Gaurav Narain

AEI, Potsdam, Germany / Kavli Institute, Beijing, China

In this paper we study the propagator of a vector fields on a
euclidean maximally-symmetric background in arbitrary space-time
dimensions. We study two cases of interest: Massive and massless
vector fields. In each case we computed the propagator of the vector
fields on euclidean deSitter background, isolating the transverse and
longitudinal part. In both case of massive and massless vector
fields, the short distance limit of the full propagator agrees with
the flat space-time propagator. In the case of massive propagator, the
transverse part has a well defined massless limit, and in this limit
it goes to the transverse propagator for the massless fields. The
transverse propagator for antipodal point separation is nonzero and
negative, but vanishes in the flat space-time limit (Ricci scalar
going to zero). The longitudinal part of the massive propagator
diverges as $1/m^2$, where $m$ is the mass of the field. The
longitudinal part of the massless propagator is gauge dependent and in
particular is proportional to the gauge parameter used in the gauge
fixing condition. It vanishes in the Landau gauge. Comparison with the
past literature is made.