We compute the structure function, transverse momentum dependent parton distributions (TMDs), and generalized parton distributions (GPDs) for the physical photon from the light-front quantum electrodynamics (QED) Hamiltonian, determined for its constituent bare photon and electron-positron Fock components within the Basis Light-Front Quantization framework. After performing nonperturbative renormalization, we obtain a good quality description of the perturbative QED properties of the photon, as well as good agreement with the experimental data for the photon's structure function. We also investigate the TMDs and GPDs of the space-like and the time-like virtual photon by incorporating a nonzero photon mass.
We present the Poincare algebra interpolating between instant and light-front time quantizations. The angular momentum operators satisfying SU(2) algebra are constructed in an arbitrary interpolation angle and shown to be identical to the ordinary angular momentum and Leutwyler-Stern angular momentum in the instant and light-front quantization limits, respectively. The exchange of the dynamical role between the transverse angular mometum and the boost operators is manifest in our newly constructed algebra.
A recent paper by Alves, Das, and Perez contains a calculation of the one-loop self-energy in ϕ^{3} field theory at T\neq 0 using light-front quantization and concludes that the self-energy is different than the conventional answer and is not rotationally invariant. The changes of variables displayed below show that despite the complicated appearance of the thermal self-energy in light-front variables, it is exactly the same as the conventional result.
We investigate the leading-twist transverse momentum-dependent distribution functions (TMDs) for a physical electron, a spin-1/2 composite system consisting of a bare electron and a photon, using the Basis Light-front Quantization (BLFQ) framework. The light-front wave functions of the physical electron are obtained from the eigenvectors of the light-front QED Hamiltonian. We evaluate the TMDs using the overlaps of the light-front wave functions. The BLFQ results are found to be in excellent agreement with those TMDs calculated using lowest-order perturbation theory.
We investigate the electromagnetic form factors of the nucleon in the framework of basis light front quantization. We compute the form factors using the light front wavefunctions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, the longitudinal confinement, and a one-gluon exchange interaction with fixed coupling. The electromagnetic radii of the nucleon are also computed.
The light-front quantization of QCD provides an alternative to lattice gauge theory for computing the mass spectrum, scattering amplitudes, and other physical properties of hadrons directly in Minkowski space. Nonperturbative light-front methods for solving gauge theory and obtaining light-front wavefunctions, such as discretized light-front quantization, the transverse lattice, and light-front resolvents are reviewed. The resulting light-front wavefunctions give a frame-independent interpolation between hadrons and their quark and gluon degrees of freedom, including an exact representation of…
We obtain the light-front wavefunctions for the nucleon in the valence quark Fock space from an effective Hamiltonian, which includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling. The wavefunctions are generated by solving the eigenvalue equation in a basis light-front quantization. Fitting the model parameters, the wavefunctions lead to good simultaneous description of electromagnetic form factors, radii, and parton distribution functions for the proton.
We introduce a new method to include condensates in the light-cone Hamiltonian. By using a Gaussian approximation to the ordinary vacuum in a theory close to the light front, we derive an effective Hamiltonian on the light cone, which has new terms reflecting the nontriviality of the vacuum. We demonstrate our method for scalar $ϕ^4$-theory and the massive Schwinger model.
We solve for the light-front wave functions (LFWFs) of the physical photon from the eigenvectors of the light-front quantum electrodynamics (QED) Hamiltonian with the aim to determine its bare photon and electron-positron Fock components. We then employ the resulting LFWFs to compute the transverse momentum dependent parton distributions (TMDs) and the generalized parton distributions (GPDs) of the photon. The TMDs are found to be in excellent agreement with the lowest-order perturbative results calculated using the electron-positron quantum fluctuation of the photon. The GPDs are also consist…
We study the unpolarized and the helicity dependent generalized parton distributions (GPDs) for the valence quarks of the proton in both momentum space and position space within the basis light-front quantization (BLFQ) framework. The GPDs for the valence quarks are computed from the eigenvectors of a light-front effective Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. Employing these GPDs, we obtain the spatial distributions of quark angular momentum inside the proton. In our BLFQ approac…
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched s…
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time cannot be transformed into each other. While they would thus appear to describe different theories, we show that this is not in fact the case. In instant-time quantization unequal instant-time commutation or anticommutation relations for free scalar, fermion, or gauge boson fields are c-numbers. We show that when these unequal instant-time commutation or anticommutation relations are evaluated at equal light-front time they are identical to t…
We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the rest…
The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor $g_{\bar{μν}}$ is non-diagonal. The Kubo, Martin, Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount $-i\big/(T\sqrt{g_{\bar{00}}})$. Light front quantization fails since $g_{\bar{00}}=0$, however various related quantizations are possible.
It is often stated that the vacuum is trivial when light-front (null-plane) quantization is applied to a quantum field theory, in contrast to the situation with equal-time quantization. In fact, it is has long been known that the statement is false, and that in certain cases the standard rules for light-front perturbation theory need modification. This paper gives an elementary review of these issues, including an explanation of how and when there is a failure of the elementary derivation of the rules for light-front perturbation theory.
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.
We obtain the distribution amplitude (DA) of the pion from its light-front wave functions in the basis light-front quantization framework. This light-front wave function of the pion is given by the lowest eigenvector of a light-front effective Hamiltonian consisting a three-dimensional confinement potential and the color-singlet Nambu--Jona-Lasinion interaction both between the constituent quark and antiquark. The quantum chromodynamics (QCD) evolution of the DA is subsequently given by the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution equation. Based on this DA, we then evaluate th…
We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extens…
While the particle-number-conserving convolution formalism established in the Drell-Yan-West reference frame is frequently used to compute exclusive amplitudes in the light-front quantization, this formalism is limited to only those frames where the light-front helicities are not changed and the good (plus) component of the current remains unmixed. For an explicit demonstration of such criteria, we present the relations between the current matrix elements in the two typical reference frames used for calculations of the exclusive amplitudes, i.e. the Drell-Yan-West and Breit frames and investig…
We present a calculation of the mass spectrum of positronium within the framework of the recently developed Basis Light-Front Quantization approach to non-perturbative quantum field theory. In this calculation, we employ a two-body effective interaction for the photon exchange, neglecting self-energy effects. We demonstrate the cancellation of Light-Front small-{\it x} divergences within our non-perturbative approach. The resulting spectrum is compared to both non-relativistic quantum mechanics and previous work in Discretized Light-Cone Quantization.
Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultra-violet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small $k^+$ modes have been effectively ``integrated out'', with an infinite number of renormali…
We employ an effective Hamiltonian that includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling constant. By solving the eigenvalue equation in basis light-front quantization (BLFQ), we generate the light-front wavefunctions (LFWFs) for the nucleon in the valence quark Fock space. Fitting the model parameters, we obtain high-quality descriptions of electromagnetic form factors and radius for proton while the results deviate somewhat from experimental data for neutron.
Basis Light-front Quantization (BLFQ) is a nonperturbative approach to quantum field theory. In this paper, we report our recent progress in applying BLFQ to the positronium system in QED and to the meson and the baryon system in QCD. We present preliminary results on the mass spectrum, light-front wave functions and other observables of these systems, where one dynamical gauge boson is retained for the positronium and meson systems.
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time not only cannot be transformed into each other, they take completely different forms. While they would thus appear to describe different theories, we show that this is not in fact the case. By looking not at equal times but at unequal times, we show that unequal instant-time commutation or anticommutation relations are completely equivalent to unequal light-front time commutation or anticommutation relations. Light-front quantization and inst…
We apply the Basis Light-Front Quantization (BLFQ) approach to the Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in light-front gauge. Based on the resulting non-perturbative ground state light-front amplitude we evaluate the electron anomalous magnetic moment. The numerical results from extrapolating to the infinite basis limit reproduce the perturbative Schwinger result with relative deviation less than 0.6%. We report significant improvements over previous works includi…
We investigate the structure of the light meson with one dynamical gluon from the light-front QCD Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock sectors, together with a three-dimensional confinement. After fitting the light meson mass spectroscopy, the light-front wave functions provide a good quality description of the pion electromagnetic form factor, and the valence quark distribution functions following QCD scale evolution.
We apply the basis light front quantization (BLFQ) approach to describe the valence structures of the charged light meson ground states. Specifically, the light front wavefunctions of $π^\pm$, $ρ^\pm$, $K^\pm$, and $K^{*\pm}$ are obtained as the eigenvectors of the light front effective Hamiltonians with confinement potentials supplemented by the color singlet Nambu--Jona-Lasinio (NJL) interactions. We adjust our model such that the spectrum of these ground states and the charge radii of the pseudoscalar states agree with experimental results. We present the elastic form factors and parton dis…
An introductory overview on Light-Front quantization, with some emphasis on recent achievements, is given. Light-Front quantization is the most promising and physical tool to study deep inelastic scattering on the basis of quark gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum effects can only appear in zero-mode degrees of freedom) and the physical basis allows for a description of hadrons that stays close to intuition. Recent progress has ben made in understanding the connection between effective LF Hamiltonians and nontrivial vacuum condesates. Discrete Light-Con…
Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton-nucleus and ultra-peripheral heavy ion collisi…
Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper we develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. We construct the most general form of the statistical operator allowed by the Poincare algebra and show that there are no zero-mode related problems when describing phase transitions. We then demonstrate a direct connection between densities in ligh…
We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Bas…
Convergence in charmonium structure: light-front wave functions from basis light-front quantization and Dyson-Schwinger equations
University of Science & Technology of China（中国科学技术大学）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽基础前沿与交叉科学研究中心）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Iowa State University（爱荷华州立大学）；Anhui University of Science and Technology（安徽理工大学）
Basis Light-Front Quantized Field Theory (BLFQ) is an $\textit{ab intio}$ Hamiltonian approach that adopts light-cone gauge, light-front quantization and state-of-the-art many-body methods to solve non-perturbative quantum field theory problems. By a suitable choice of basis, BLFQ retains the underlying symmetries to the extent allowed within light-front coordinates. In this talk, we outline the scheme for applying BLFQ to QCD bound state problems. We adopt a 2D Harmonic Oscillator with 1D plane wave basis that corresponds to the AdS/QCD soft-wall solution. Exact treatment of the symmetries wi…
We investigate the parton distribution functions (PDFs) of the pion and kaon from the eigenstates of a light-front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolving, are consistent with the E615 experiment at Fermilab. In addition, the ratio of the up quark distribution in the kaon to that in the pion also agrees with the NA3 experimental result at CERN.
The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and to define a kinematical definition of angular momentum. The AdS/CFT correspondence of large $N_C$ supergravity theory in higher-d…
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis carefully. The decomposition of the fields into positive and negative frequency terms needs to be done carefully after which we show that the (anti) commutation relations for the quantum operators become frame independent. The frame dependence is completely contained in the functions multiplying these operators in the field decomposition. We derive the propagators f…
We calculate the electromagnetic (charge, magnetic and quadrupole) form factors and the associated static moments of heavy quarkonia (charmonia and bottomonia) using the Basis Light Front Quantization (BLFQ) approach. For this work, we adopt light front wavefunctions (LFWFs) generated by a holographic QCD confining potential and a one-gluon exchange interaction with fixed coupling. We compare our BLFQ results with the limiting case of a single BLFQ basis state description of heavy quarkonia and with other available results. These comparisons provide insights into relativistic effects. Using th…
We find a correspondence between semiclassical QCD quantized on the light-front and a dual gravity model in anti--de Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence -- light-front holography -- leads to a light-front Hamiltonian and relativistic bound-state wave equations that are functions of an invariant impact variable $ζ$ which measures the separation of the quark and gluonic constituents within hadrons at equal light-front time. The eigenvalues of the resulting light-front Schrödinger and Dirac equations are consistent…
We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu--Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion str…
Even though the Drell-Yan-West formulation is the most rigorous and well-established framework to compute the exclusive processes, its utility has been limited only to the spacelike region because of the intrinsic kinematic constraint $q^+=0$. We present an explicit example demonstrating how one may obtain the necessary information (i.e. nonvalence or so called Z-graph contribution) in the timelike region of exclusive process without encountering a formidable task of direct calculation that has hindered so far the progress in this area. In the analysis of $q\bar{Q}$ bound state form factors us…
We study the structure of scalar field light front quantization vacuum graphs. In instant time quantization both non-vacuum and vacuum graphs can equivalently be described by either the off-shell four-dimensional Feynman diagram approach or the on-shell three-dimensional Fock space approach, with this being the case since the relevant Feynman diagrams are given entirely by pole terms. This is also the case for light front quantization non-vacuum graphs. However this is the not the case for light front vacuum sector diagrams, since then there are also circle at infinity contributions to Feynman…
Transverse force tomography inside a proton from Basis Light-front Quantization
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学技术大学核科学与技术学院）
The Casimir force between conducting plates at rest in an inertial frame is usually computed in equal-time quantization, the natural choice for the given boundary conditions. We show that the well-known result obtained in this way can also be obtained in light-front quantization. This differs from a light-front analysis where the plates are at "rest" in an infinite momentum frame, rather than an inertial frame; in that case, as shown by Lenz and Steinbacher, the result does not agree with the standard result. As is usually done, the analysis is simplified by working with a scalar field and per…
The spontaneous symmetry breaking (and Higgs) mechanism in the theory quantized on the light-front ({\it l.f.}), in the {\it discretized formulation}, is discussed. The infinite volume limit is taken to obtain the {\it continuum version}. The hamiltonian formulation is shown to contain a new ingredient in the form of nonlocal {\it constraint eqs.} which lead to a {\it nonlocal l.f. Hamiltonian}. The description of the broken symmetry here has the same physical content as in the conventional formulation though arrived at through a different mechanism.
Gravitational form factors of light mesons from Basis Light-Front Quantization
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Physics, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
The light-front (LF) canonical quantization of quantum chromodynamics in covariant gauge is discussed. The Dirac procedure is used to eliminate the constraints in the gauge-fixed front form theory quantum action and to construct the LF Hamiltonian formulation. The physical degrees of freedom emerge naturally. The propagator of the dynamical $ψ_+$ part of the free fermionic propagator in the LF quantized field theory is shown to be causal and not to contain instantaneous terms. Since the relevant propagators in the covariant gauge formulation are causal, rotational invariance---including the Co…
Light-Front quantization is one of the most promising and physical tools towards studying deep inelastic scattering on the basis of quark gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum effects can only appear in zero-mode degrees of freedom) and the physical basis allows for a description of hadrons that stays close to intuition. I am reviewing recent progress in understanding the deep connection between renormalization of light-front Hamiltonians, effective light-front Hamiltonians and nontrivial vacuum condensates.
The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter ζ= Q^2/ 2 p.q can be used to provide an image of the target hadron in the boost-invariant variable σ, the coordinate conjugate to light-front time τ=t+ z/ c. As an illustration, we construct a consistent covariant model of the DVCS amplitude and its associated generalized parton distributions using the quantum fluctuations of a fermion state at one loop in QED, thus providing a representation of the light-front wavefunctions of a lepton in σspace. A consistent model for hadron…
