Interpolating the 't Hooft model between Instant Form dynamics and Light-Front dynamics in the Coulomb gauge

The 1+1D model of quantum chromodynamics (QCD) in the infinite number of colors, or ‘t Hooft model, is interpolated between the instant form dynamics (IFD) and the light-front dynamics (LFD) using an interpolation parameter δ in the interpolating Coulomb gauge which links the Coulomb gauge (A⁰ = 0) in IFD and the light-front gauge (A+ = 0). While calculations such as these were performed [1] in the interpolating axial gauge which links the spatial or axial gauge (A1 = 0) in IFD and the light-front gauge (A+ = 0), there are a number of benefits to the Coulomb gauge that cannot be ignored. All degrees of freedom are physical, making this an ideal choice for finding the bound-state equations and for renormalizability. Using this parameter δ, we find the mass gap equation using both hamiltonian formalism and feynman diagram analysis, noting that it reproduces both the results for IFD and LFD in the Coulomb gauge and the light-front gauge, respectively. We then derive the quark-antiquark bound-state equation in the interpolating dynamics using the dressed fermion propagator and compare with results obtained in the interpolating axial gauge [1]. The meson mass spectra of such mesons that follow Regge trajectories are independent of δ, which are observed in both IFD and LFD calculations using the interpolating axial gauge condition. We also obtain the bound-state wave functions in the interpolating dynamics. These wavefunctions are particularly useful in the calculation of quasi-parton distribution functions (quasi-PDFs), in which we can produce an alternative approach to the quasi-PDFs not only with the frame dependence but also with the δ dependence. The Coulomb gauge in IFD is particularly interesting in this way, because the A0 component is renormalization group invariant [2]. Thus, the interpolation may lead to an alternative quasi-PDF that can be implemented in the lattice QCD without suffering from the large momentum boost.

1. Ma, Bailing, and Chueng-Ryong Ji. “Interpolating ’t Hooft Model between Instant and Front Forms.”

Physical Review D, vol. 104, no. 3, 2021,

https://doi.org/10.1103/physrevd.104.036004.

2. Zwanziger, D. (1998). Coulomb-Gauge in QCD: Renormalization and confinement.

Progress of Theoretical Physics Supplement, 131, 233-242.

https://doi.org/10.1143/ptps.131.233