Interpolation from Instant Form Dynamics to Light-Front Dynamics and Update on Light-Front Quark Model Analysis in Meson Phenomenology.

摘要

In this dissertation, we present the interpolation of the quantum electrodynamics (QED) theory between the instant form and the front form of relativistic Hamiltonian dynamics. A unified general physical gauge that interpolates between the Coulomb gauge in the instant form dynamics (IFD) and the light-front gauge in the light-front dynamics (LFD) is obtained. Photon polarization vectors and corresponding photon propagator for any interpolation angle are derived. Using these results, we calculate time-order scattering amplitudes for an arbitrary interpolation angle. The emerged universal J-shaped correlation between the total momentum of the system and the interpolation angle, coined as the "J-curve", characterizes how the IFD changes to the LFD. We discuss the singular behavior of this correlation in conjunction with the zero-mode issue in LFD.;We also derive the generalized helicity spinor in the (0, J)⊕( J, 0) chiral representation that naturally links the instant form helicity spinors and the light-front spinor as well as the generalized Melosh transformation that relates these generalized helicity spinors to the usual Dirac spinors. Our analysis of the spin orientation angle reveals that its behavior as a function of the momentum direction is bifurcated at a critical interpolation angle and the IFD and the LFD separately belong to the two different branches. In conjunction with the bifurcation of branches, two boundaries appear in the interpolating helicity amplitudes and the same J-curve persists within these two boundaries. These interpolating amplitudes provide examples of broken reflection symmetry under the longitudinal boost, P z ↔ Pz, and clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame (IMF) and the LFD.;To conclude this interpolation study, we give the full Feynman rules for interpolating time-ordered diagrams in QED, including the interpolation of time-ordered fermion propagators. The canonical field theory approach is explored and the interpolating QED Hamiltonian is obtained.;We end this dissertation with an updated analysis of our light-front quark model (LFQM) for ground state pseudoscalar and vector mesons, using the variational principle to compute mass spectra and decay constants with the QCD-motivated effective Hamiltonian including a smeared out hyperfine interaction. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of (o,&phis;) and (eta,eta').