2012/12/13 by M. Beneke, P. Moch · 1 citation
Physics and Astronomy · #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.87.064018
LaTeX, 15 pages
arxiv created 2012/12/13 · arxiv updated 2015/06/12
We consider the perturbative treatment of the minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing work of Rajaraman, we obtain the dynamical mass m2 ∝ sqrtlambda H2 of the scalar for non-vanishing Lagrangian masses and the first perturbative quantum correction in the massless case. We develop the rules of a systematic perturbative expansion, which treats the zero-mode non-perturbatively, and goes in powers of sqrtlambda. The infrared divergences are self-regulated by the zero-mode dynamics. Thus, in Euclidean de Sitter space the interacting, massless scalar field is just as well-defined as the massive field. We then show that the dynamical mass can be recovered from the diagrammatic expansion of the self-energy and a consistent solution of the Schwinger-Dyson equation, but requires the summation of a divergent series of loop diagrams of arbitrarily high order. Finally, we note that the value of the long-wavelength mode two-point function in Euclidean de Sitter space agrees at leading order with the stochastic treatment in Lorentzian de Sitter space, in any number of dimensions.