Interpolating Scattering Amplitudes between Instant Form and Front Form of Relativistic Dynamics

摘要

Among the three forms of relativistic Hamiltonian dynamics proposed by Diracin 1949, the instant form and the front form can be interpolated by introducingan interpolation angle between the ordinary time $t$ and the light-front time$(t+z/c)/\sqrt{2}$. Using this method, we introduce the interpolatingscattering amplitude that links the corresponding time-ordered amplitudesbetween the two forms of dynamics and provide the physical meaning of thekinematic transformations as they allow the invariance of each individualtime-ordered amplitude for an arbitrary interpolation angle. In particular, itexhibits that the longitudinal boost is kinematical only in the front formdynamics, or the light-front dynamics (LFD), but not in any other interpolationangle dynamics. It also shows that the disappearance of the connectedcontributions to the current arising from the vacuum occurs when theinterpolation angle is taken to yield the LFD. Since it doesn't require theinfinite momentum frame (IMF) to show this disappearance and the proof isindependent of reference frames, it resolves the confusion between the LFD andthe IMF. The well-known utility of IMF usually discussed in the instant formdynamics is now also extended to any other interpolation angle dynamics usingour interpolating scattering amplitudes.