Fluctuations of the Metric Tensor: On Fermion Propagators and on the Cosmological Constant

Abstract

Conformal fluctuations of the metric tensor are considered. They give rise to a Planck scale size lower bound of the proper length. Infinit ies arising fro m the point-like character of particles are thus avoided, expressions related to fermion propagators are finite without the need to renormalize or regularize. The quark condensate, constituent quark mass, pion mass, and pion weak decay constant are calculated within the SU(2) Nambu--Jona-Lasinio model. The nu merical values are con- sistent with known strong interaction physics if one assumes very small values of the current quark mass and effective coupling constant. The usual values of these quantities in hadron phenomenology can be interpreted as resulting fro m dressing of the very s mall bare quantities with the fluctuations. With respect to the cosmological constant it is shown that a cosmological constant term, wh ich may initially exist in the gravitational action, is "masked" by the fluctuations of the metric, i.e., it does not appear in the final Einstein equation. Instead, the fluctuations give rise to a cosmological constant themselves.