Gravitational Field Excitation from the First Term ofQuantum Wilson Loop

Abstract

In 4-dimensional R-gravity, using the linear and squareterms of the expanding expression of the space-time connection,we calculate the possible curvature excitation (orderk4) of gravitational field, which is given by the first term ofquantum Wilson loop ⟨w⟩ through two-pointGreen's function of the connection. At the same time using thetree diagram propagators of gravitons, the lowest order (k4) correction to ⟨w⟩ is also calculated throughthe graviton self-energy in the term. Under the accuracy conditionup to order k4, we have obtained a complete expression of theexcitation contributed from the leading term ⟨w(2)⟩ of ⟨w⟩.