Interpolation of Quantum Chromodynamics in 1+1 Dimension

Having interpolated the quantum electrodynamics in the previous chapter, we now present the interpolation of the 't Hooft model, i.e. the two-dimensional quantum chromodynamics in the limit of infinite number of colors which is adopted from our published work Phys. Rev. D104, 036004(2021). With an angle parameter delta between delta = 0 for the instant form dynamics (IFD) and delta = pi/4 for the light-front dynamics (LFD) we formulate the interpolating mass gap equation which takes into account the non-trivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions not only reproduce the previous IFD result at delta = 0 as well as the previous LFD result at delta = p/4 but also link them together between the IFD and LFD results with the d parameter. We find the interpolation angle independent characteristic energy function which satisfies the energy-momentum dispersion relation of the dressed fermion, identifying the renormalized fermion mass function and the wavefunction renormalization factor. The renormalized fermion condensate is also found independent of d, indicating the persistence of the non-trivial vacuum structure even in the LFD. Using the dressed fermion propagator interpolating between IFD and LFD, we derive the corresponding quark-antiquark bound-state equation in the interpolating formulation verifying its agreement with the previous bound-state equations in the IFD and LFD at delta = 0 and delta = pi/4, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the delta-parameter reproducing the previous results in LFD and IFD for the equal mass quark and antiquark bound-states. The Gell-Mann-Oakes-Renner relation for the pionic ground state in the zero fermion mass limit is confirmed indicating that the spontaneous breaking of the chiral symmetry occurs in the 't Hooft model regardless of the quantization for 0 <= delta <= pi/4. We obtain the corresponding bound-state wavefunctions and discuss their reference frame dependence with respect to the frame independent LFD result. Applying them for the computation of the so-called quasi-parton distribution functions now in the interpolating formulation between IFD and LFD, we note a possibility of utilizing not only the reference frame dependence but also the interpolation angle dependence to get an alternative effective approach to the LFD-like results.