Frame-dragging effects in the gravitational quantum field theory

Analogous to magnetism in electrodynamics, it is gravitomagnetism in relativistic gravity. Since gravity determines locally inertial frames, in general relativity (GR) and other relativistic theories of gravity, frame-dragging with source motion plays key role in gravitomagnetism. Recently, Wu has put forward a gauge theory of gravity, called the gravitational quantum field theory (GQFT) with the gravitational force and the spin gauge force described by the gauge fields. Gao {\it et al.} ({\it Phy. Rev. D 109, 064072}) have derived the Shapiro time delay in the GQFT and give an empirical constraint from Cassini experimental result on the dimensionless GQFT parameter $\gamma_W$ to be $(2.1\pm 2.3)\times 10^{-5}$. In this work, we derive the frame-dragging Lense-Thirring effects in the GQFT. The current precision of LARES-LAGEOS Lense-Thirring measurement gives a constraint on $|\gamma_W|$ to be less than $2\times 10^{-2}$. This constraint is consistent with but subdominant to the Cassini experimental constraint. As a candidate of quantum gravity, we do not expect that the deviation from the GR value ($\gamma_W=0$) is large classically. With the launch of LARES 2, the precision of Lense-Thirring measurement is expected to increase by one order of magnitude in a couple of years. As to the Shapiro effect, current technologies have the capability to measure the $\gamma_W$ parameter to precision of $10^{-9}$.