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

Conformal fluctuations of the metric tensor are considered. They give rise to a Planck scale size lower bound of the proper length. Infinities arising from 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 numerical values are consistent 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 from dressing of the very small bare quantities with the fluctuations. With respect to the cosmological constant it is shown that a cosmological constant term, which 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.