Perturbative Quantum Gravity and Yang-Mills Theories in de Sitter Spacetime

This thesis consists of three parts. In the rst part we review the quantization
of Yang-Mills theories and perturbative quantum gravity in curved spacetime.
In the second part we calculate the Feynman propagators of the Faddeev-
Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the
covariant gauge. In the third part we investigate the physical equivalence of
covariant Wightman graviton two-point function with the physical graviton
two-point function.
The Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills
theories and perturbative quantum gravity in the covariant gauge are infrared
(IR) divergent in de Sitter spacetime. We point out, that if we regularize
these divergences by introducing a nite mass and take the zero mass limit
at the end, then the modes responsible for these divergences will not contribute
to loop diagrams in computations of time-ordered products in either
Yang-Mills theories or perturbative quantum gravity. We thus nd eective
Feynman propagators for ghosts in Yang-Mills theories and perturbative
quantum gravity by subtracting out these divergent modes.
It is known that the covariant graviton two-point function in de Sitter
spacetime is infrared divergent for some choices of gauge parameters. On
the other hand it is also known that there are no infrared problems for the
physical graviton two-point function obtained by xing all gauge degrees
of freedom, in global coordinates. We show that the covariant Wightman
graviton two-point function is equivalent to the physical one in the sense
that they result in the same two-point function of any local gauge-invariant
quantity. Thus any infrared divergence in the Wightman graviton two-point
function in de Sitter spacetime can only be an gauge artefact.