@article{ma_ji_2021, title={Interpolating 't Hooft model between instant and front forms}, volume={104}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.104.036004}, abstractNote={The ’t Hooft model, i.e. the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter δ between δ = 0 for the instant form dynamics (IFD) and δ = π/4 for the light-front dynamics (LFD). With this parameter δ, 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 δ = 0 as well as the previous LFD result at δ = π/4 but also link them together between the IFD and LFD results with the δ 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 wave function renormalization factor. The renormalized fermion condensate is also found independent of δ, 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 δ = 0 and δ = π/4, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the δ-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 ≤ δ ≤ π/4. We obtain the corresponding bound-state wave functions 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.}, number={3}, journal={PHYSICAL REVIEW D}, author={Ma, Bailing and Ji, Chueng-Ryong}, year={2021}, month={Aug} }
 @article{ma_ji_2020, title={Interpolating QCD(2) between the Instant and Front Forms of Relativistic Dynamics}, volume={2249}, ISSN={["0094-243X"]}, DOI={10.1063/5.0008605}, abstractNote={The two-dimensional quantum chromodynamics (QCD2) in the limit of infinite number of colors, known as ‘t Hooft model, was originally formulated in the Light Front Dynamics (LFD). The theory is exactly solvable, while still bearing some resemblance to the four-dimensional real world QCD in aspects such as confinement and mass g ap, as well as the spontaneous breaking of chiral symmetry. The work in the Instant Form Dynamics (IFD) was done in 1978 by Bars and Green. The quark- antiquark bound state equation was derived and solved in each of the two forms, i.e., ‘t Hooft equation and Bars-Green equations, respectively, and they give the same discrete meson mass spectrum independent of the quantization form as expected. Introducing an interpolation angle parameter δ, in this work, we link the two distinct forms of dynamics, IFD and LFD, by letting the space-time axes rotate from the ordinary equal-time form {t, x} to the light front{x+,x−}, as δ varies from 0 to π/4. We unify the ‘t Hooft and Bars-Green equations into one formula, and by numerically solving it we confirm the independence of the meson mass spectra on the interpolation angle δ. We note that the quark condensate is quantization angle independent. This indicates a non-trivial vacuum structure even in the light-front form.}, journal={PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON MESON-NUCLEON PHYSICS AND THE STRUCTURE OF THE NUCLEON}, author={Ma, Bailing and Ji, Chueng-Ryong}, year={2020} }
 @article{ji_li_ma_suzuki_2018, title={Interpolating Quantum Electrodynamics}, volume={59}, ISSN={["1432-5411"]}, DOI={10.1007/s00601-018-1397-4}, abstractNote={We discuss the interpolation between the instant form dynamics (IFD) and the light-front dynamics (LFD) proposed by Dirac in 1949 and present its application to quantum electrodynamics (QED). Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the IFD at infinite momentum frame and the LFD. Entwining the fermion propagator interpolation with our previous works of the interpolating helicity spinors and the electromagnetic gauge field interpolation, we fasten the bolts and nuts necessary to launch the interpolating QED at least in the tree level.}, number={5}, journal={FEW-BODY SYSTEMS}, author={Ji, Chueng-Ryong and Li, Ziyue and Ma, Bailing and Suzuki, Alfredo Takashi}, year={2018}, month={Sep} }
 @article{ji_li_ma_suzuki_2018, title={Interpolating quantum electrodynamics between instant and front forms}, volume={98}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.98.036017}, abstractNote={The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $\delta$ spanning between the instant form dynamics (IFD) at $\delta =0$ and the front form dynamics which is now known as the light-front dynamics (LFD) at $\delta =\pi/4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed in our previous work, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as $e^+ e^- \to \gamma \gamma$ and $e \gamma \to e \gamma$ and present the whole landscape of the scattering amplitudes in terms of the frame dependence or the scattering angle dependence with respect to the interpolating angle dependence. Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame approach and the LFD.}, number={3}, journal={PHYSICAL REVIEW D}, author={Ji, Chueng-Ryong and Li, Ziyue and Ma, Bailing and Suzuki, Alfredo Takashi}, year={2018}, month={Aug} }