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

TL;DR

This thesis investigates infrared divergences in quantum field theories in de Sitter spacetime, showing they are gauge artifacts and proposing effective propagators by regularizing divergences.

Contribution

It demonstrates the gauge nature of infrared divergences in graviton two-point functions and introduces effective propagators for ghosts by regularizing IR divergences.

Findings

Infrared divergences in ghost propagators are regularized by finite mass subtraction.

Covariant Wightman graviton two-point function is gauge equivalent to the physical one.

Infrared divergences in graviton two-point functions are gauge artifacts.

Abstract

This thesis consists of three parts. In the first 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 finite 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 find effective 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 fixing 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.