Light-front Quantization Research Articles

Basis Light-Front Quantization: Recent Progress and Future Prospects

Light-front Hamiltonian field theory has advanced to the stage of becoming a viable non-perturbative method for solving forefront problems in strong interaction physics. Physics drivers include hadron mass spectroscopy, generalized parton distribution functions, spin structures of the hadrons, inelastic structure functions, hadronization, particle production by strong external time-dependent fields in relativistic heavy ion collisions, and many more. We review selected recent results and future prospects with basis light-front quantization that include fermion-antifermion bound states in QCD, fermion motion in a strong time-dependent external field and a novel non-perturbative renormalization scheme.

Form factors and generalized parton distributions in basis light-front quantization

We calculate the elastic form factors and the Generalized Parton Distributions (GPDs) for four low-lying bound states of a demonstration fermion-antifermion system, strong coupling positronium ($e \bar{e}$), using Basis Light-Front Quantization (BLFQ). Using this approach, we also calculate the impact-parameter dependent GPDs $q(x, {\vec b_\perp})$ to visualize the fermion density in the transverse plane (${\vec b_\perp}$). We compare selected results with corresponding quantities in the non-relativistic limit to reveal relativistic effects. Our results establish the foundation within BLFQ for investigating the form factors and the GPDs for hadronic systems.

Light-front quantization with the light cone gauge

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first-class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang–Mills theory and the superparticle in a 2+1-dimensional target space.

Non-perturbative Renormalization in Truncated Yukawa Model

An approach to non-perturbative calculations in the light-front quantum field theory and its new developments are briefly reviewed. We start with the decomposition of the state vector in Fock components. After truncation of this decomposition (main approximation in this approach), the eigenvalue equation for the light-front Hamiltonian generates, in Minkowski space, a finite system of integral equations for the Fock components. Solving this system numerically and performing the non-perturbative renormalization, we find the state vector of fermion in the quenched scalar Yukawa model, up to the four-body truncation (one fermion \(+\) three bosons), for rather large values of the coupling constant. With the state vector, found in this way, the fermion electromagnetic form factors are calculated. Comparing results obtained in the four-body truncation with those found in the previous, three-body truncation, we discover very good convergence relative to truncation, that indicates that we are close to the exact non-perturbative solution in this field-theoretical model. The approach can be extended to more realistic field theories and, after further development, it could constitute an alternative to the lattice calculations.

The pion electromagnetic structure with self-energy

We study the electromagnetic structure of the pion in terms of the quantum cromodynamic (QCD) model on the Breit-frame. We calculated the observables, such as the electromagnetic form factor. The priori to have a calculation covariant need to get the valence term of the eletromagnetic form factor. We use the usual formalism in quantum field theory (QFT) and light-front quantum field theory (LFQFT) in order to test the properties of form factor in nonperturbative QCD. In this particular case, the form factor can be obtained using the pion Light-Front (LF) wave function including self-energy from Lattice-QCD. Specifically, these calculations was performed in LF formalism. We consider a quark-antiquark vertex model having a quark self-energy. Also we can use other models to compare the pion electromagnetic form factor with different wave function and to observe the degree of agreement between them.

Light-Front Holography, Color Confinement, and Supersymmetric Features of QCD

Light-Front Quantization provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography -- the duality between the front form and AdS$_5$, the space of isometries of the conformal group. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons of the same parity. The mass scale $\kappa$ underlying confinement and hadron masses can be connected to the parameter $\Lambda_{\overline {MS}}$ in the QCD running coupling by matching the nonperturbative dynamics, as described by the effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The result is an effective coupling defined at all momenta. This matching of the high and low momentum transfer regimes determines a scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of $Q_0$ to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality (PMC) for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the front-form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.

Light-Front Quantization of the Vector Schwinger Model with a Photon Mass Term in Faddeevian Regularization

In this talk, we study the light-front quantization of the vector Schwinger model with photon mass term in Faddeevian Regularization, describing two-dimensional electrodynamics with mass-less fermions but with a mass term for the U(1) gauge field. This theory is gauge-non-invariant (GNI). We construct a gauge-invariant (GI) theory using Stueckelberg mechanism and then recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-fixing conditions (GFC’s). We then study LFQ of this new GI theory.

Light-Front Quantization of the Restricted Gauge Theory of QCD 2

In this talk we study the light-front quantization of the restricted gauge theory of QCD2a la Cho et al.

Spin decomposition of the electron in QED

We perform a systematic study on the spin decomposition of an electron in QED at one-loop order. It is found that the electron orbital angular momentum defined in Jaffe-Manohar and Ji spin sum rules agrees with each other, and the so-called potential angular momentum vanishes at this order. The calculations are performed in both dimensional regularization and Pauli-Villars regularization for the ultraviolet divergences, and they lead to consistent results. We further investigate the calculations in terms of light-front wave functions, and find a missing contribution from the instantaneous interaction in light-front quantization. This clarifies the confusing issues raised recently in the literature on the spin decomposition of an electron, and will help to consolidate the spin physics program for nucleons in QCD.

Heavy quarkonium in a holographic basis

We study the heavy quarkonium within the basis light-front quantization approach. We implement the one-gluon exchange interaction and a confining potential inspired by light-front holography. We adopt the holographic light-front wavefunction (LFWF) as our basis function and solve the non-perturbative dynamics by diagonalizing the Hamiltonian matrix. We obtain the mass spectrum for charmonium and bottomonium. With the obtained LFWFs, we also compute the decay constants and the charge form factors for selected eigenstates. The results are compared with the experimental measurements and with other established methods.

Limit transition to the light-front QCD and a quark–antiquark approximation

We consider a transition to the light-front quantum chromodynamics from theories quantized on spacelike planes that approach the light front. This limit transition differs for zero and nonzero modes, which leads to the appearance of a semiphenomenological parameter that can be used to describe confinement effects. As an illustration, we consider the problem of the bound states of a quark–antiquark pair in 2+1 dimensions. We use a lattice gauge-invariant regularization in the transverse space and consequently obtain an analogue of the’ t Hooft equation. We also discuss the possibility of calculating the spectrum of bound states in 3+1 dimensions.

Advances in Basis Light-Front Quantization

Basis Light-front Quantization has been developed as a first-principles nonperturbative approach to quantum field theory. In this article we report our recent progress on the applications to the single electron and the positronium system in QED. We focus on the renormalization procedure in this method.

Solvable Models with Massless Light-Front Fermions

Two-dimensional models with massless fermions (Thirring model, Thirring–Wess and Schwinger model, among others) have been solved exactly a long time ago in the conventional (space-like) form of field theory and in some cases also in the conformal field theoretical approach. However, solutions in the light-front form of the theory have not been obtained so far. The primary obstacle is the apparent difficulty with light-front quantization of free massless fermions, where one half of the fermionic degrees of freedom seems to “disappear” due to the structure of a non-dynamical constraint equation. We shall show a simple way how the missing degree of freedom can be recovered as the massless limit of the massive solution of the constraint. This opens the door to the genuine light front solution of the above models since their solvability is related to free Heisenberg fields, which are the true dynamical variables in these models. In the present contribution, we give an operator solution of the light front Thirring model, including the correct form of the interacting quantum currents and of the Hamiltonian. A few remarks on the light-front Thirring–Wess models are also added. Simplifications and clarity of the light-front formalism turn out to be quite remarkable.

Basis light-front quantization approach to positronium

We present the first application of the recently developed Basis Light-Front Quantization (BLFQ) method to self-bound systems in quantum field theory, using the positronium system as a test case. Within the BLFQ framework, we develop a two-body effective interaction, operating only in the lowest Fock sector, that implements photon exchange, neglecting fermion self-energy effects. We then solve for the mass spectrum of this interaction at the unphysical coupling $\alpha=0.3$. The resulting spectrum is in good agreement with the expected Bohr spectrum of non-relativistic quantum mechanics. We examine in detail the dependence of the results on the regulators of the theory.

Hamiltonian, path integral and BRST formulations of large $$N$$ N scalar QCD $$_{2}$$ 2 on the light-front and spontaneous symmetry breaking

Recently Grinstein, Jora, and Polosa have studied a theory of large-$N$ scalar quantum chromodynamics in one-space one-time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of $SU(N)$ and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge-invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge.

The common elements of atomic and hadronic physics

Atomic physics and hadronic physics are both governed by the Yang Mills gauge theory Lagrangian; in fact, Abelian quantum electrodynamics can be regarded as the zero-color limit of quantum chromodynamics. I review a number of areas where the techniques of atomic physics can provide important insight into hadronic eigenstates in QCD. For example, the Dirac-Coulomb equation, which predicts the spectroscopy and structure of hydrogenic atoms, has an analog in hadron physics in the form of frame-independent light-front relativistic equations of motion consistent with light-front holography which give a remarkable first approximation to the spectroscopy, dynamics, and structure of light hadrons. The production of antihydrogen in flight can provide important insight into the dynamics of hadron production in QCD at the amplitude level. The renormalization scale for the running coupling is unambiguously set in QED; an analogous procedure sets the renormalization scales in QCD, leading to scheme-independent scale-fixed predictions. Conversely, many techniques which have been developed for hadron physics, such as scaling laws, evolution equations, the quark-interchange process and light-front quantization have important applicants for atomic physics and photon science, especially in the relativistic domain.

The Light-Front Schrödinger Equation and the Determination of the Perturbative QCD Scale from Color Confinement: A First Approximation to QCD

The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$ has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number $n$ and orbital angular momentum $L$. Only one mass parameter $\kappa$ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale $\kappa$ underlying confinement and hadron masses determines the scale $\Lambda_{\overline{MS}} $ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value $\Lambda_{\overline{MS}} = 0.328 \pm 0.034$ GeV is in agreement with the world average $0.339 \pm 0.010$ GeV. The analysis applies to any renormalization scheme.

Light-front holography and superconformal quantum mechanics: A new approach to hadron structure and color confinement

A primary question in hadron physics is how the mass scale for hadrons consisting of light quarks, such as the proton, emerges from the QCD Lagrangian even in the limit of zero quark mass. If one requires the effective action which underlies the QCD Lagrangian to remain conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory, then a unique, color-confining potential with a mass parameter [Formula: see text] emerges. The actual value of the parameter [Formula: see text] is not set by the model – only ratios of hadron masses and other hadronic mass scales are predicted. The result is a nonperturbative, relativistic light-front quantum mechanical wave equation, the Light-Front Schrödinger Equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the identical slope in the radial quantum number [Formula: see text] and orbital angular momentum [Formula: see text]. The same light-front equations for mesons with spin [Formula: see text] also can be derived from the holographic mapping to QCD (3+1) at fixed light-front time from the soft-wall model modification of AdS5 space with a specific dilaton profile. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. One can also extend the analysis to baryons using superconformal algebra – [Formula: see text] supersymmetric representations of the conformal group. The resulting fermionic LF bound-state equations predict striking similarities between the meson and baryon spectra. In fact, the holographic QCD light-front Hamiltonians for the states on the meson and baryon trajectories are identical if one shifts the internal angular momenta of the meson ([Formula: see text]) and baryon ([Formula: see text]) by one unit: [Formula: see text]. We also show how the mass scale [Formula: see text] underlying confinement and the masses of light-quark hadrons determines the scale [Formula: see text] controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The data for the effective coupling defined from the Bjorken sum rule [Formula: see text] are remarkably consistent with the Gaussian form predicted by LF holographic QCD. The result is an effective coupling defined at all momenta. The predicted value [Formula: see text] is in agreement with the world average [Formula: see text]. We thus can connect [Formula: see text] to hadron masses. The analysis applies to any renormalization scheme.

Light-Front Quantization with Explicit Lorentz Symmetry for Yukawa Model

The Dirac method for constrained systems is incomplete for the light-front (LF) quantization of the Yukawa model in D = 1 + 1 dimensions. A novel quantization procedure is proposed, where one obtains the LF commutator and anti-commutators directly from the Heisenberg equations generated by P+, which is a kinematical operator. By adding the general assumptions on the quantum field theory, one evalutes 2-point Wightman functions for a free field case. The Lorentz symmetry is manifest at every step of this novel LF procedure. The Gaussian effective potential is defined with the point-splitting regularization with a space-like separation. The optimum values of the mass parameters are regularization independent.

Application of Coherent State Approach for the Cancellation of Infrared Divergences to All Orders in LFQED

We sketch an all order proof of cancellation of infrared (IR) divergences in Light Front Quantum Electrodynamics (LFQED) using a coherent state formalism. In this talk, it has been shown that the true IR divergences in fermion self energy are eliminated to all orders in a light-front time-ordered perturbative calculation if one uses coherent state basis instead of the usual Fock basis to calculate the Hamiltonian matrix elements.