Nonperturbative light-front Hamiltonian methods

Abstract

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 scalar Yukawa theory, ${\varphi }^4$ theory, ordinary Yukawa theory, supersymmetric Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

67 pages, 14 figures; review to appear in Progress in Particle and Nuclear Physics

References in corpus (156)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Generalized Parton Distributions
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Unraveling hadron structure with generalized parton distributions
• Hard Exclusive Reactions and the Structure of Hadrons
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Dyson-Schwinger equations: a tool for hadron physics
• Light-Front Holographic QCD and Emerging Confinement
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Infrared Properties of QCD from Dyson-Schwinger equations
• Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems
• Explanation and Prediction of Observables using Continuum Strong QCD
• Nonperturbative Light-Front QCD
• The Lee-Wick Standard Model
• Ab initio no-core full configuration calculations of light nuclei
• Hamiltonian light-front field theory in a basis function approach
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Aspects of Hadron Physics
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Heavy Quarkonium in a Holographic Basis
• A Cheap Alternative to the Lattice?
• Light Front Quantization
• Compactification in the Lightlike Limit
• Basis Light-Front Quantization Approach to Positronium
• Random phase vector for calculating the trace of a large matrix
• Systematic renormalization scheme in light-front dynamics with Fock space truncation
• Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics
• Low Temperature Lanczos Method
• Electron g-2 in Light-Front Quantization
• The Vector Meson Form Factor Analysis in Light-Front Dynamics
• Mass Spectra of Supersymmetric Yang-Mills Theories in 1+1 Dimensions
• Aspects of Chern-Simons Theory
• Nonvanishing zero modes in the light-front current
• Quarkonia in Hamiltonian Light-Front QCD
• Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
• Scattering in Time-Dependent Basis Light-Front Quantization
• Spontaneous Symmetry Breaking at Infinite Momentum without P+ Zero-Modes
• Electron in a transverse harmonic cavity
• Minimal Lee-Wick Extension of the Standard Model
• Transverse lattice calculation of the pion light-cone wavefunctions
• Light Front Quantization--A Technique for Relativistic and Realistic Nuclear Physics
• A renormalization group approach to Hamiltonian light-front field theory
• Initial bound state studies in light-front QCD
• A light-front coupled-cluster method for the nonperturbative solution of quantum field theories
• The Relativistic Bound State Problem in QCD: Transverse Lattice Methods
• Spontaneous symmetry breaking of (1+1)-dimensional ${\varphi }^4$ theory in light-front field theory (II)
• A nonperturbative calculation of the electron's magnetic moment
• Pauli--Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization
• Spontaneous symmetry breaking of (1+1)-dimensional ${\varphi }^4$ theory in light-front field theory (III)
• Towards a SDLCQ test of the Maldacena Conjecture
• Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons
• Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front
• Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates
• Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model
• Kinks in Discrete Light Cone Quantization
• Analytic Treatment of Positronium Spin Splittings in Light-Front QED
• Covariance of Light-Front Models: Pair Current
• Nonperturbative renormalization and the electron's anomalous moment in large-alpha QED
• Non-perturbative quantum time evolution on the light-front
• Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
• Many-body Fock sectors in Wick-Cutkosky model
• Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model
• Two-fermion relativistic bound states in Light-Front Dynamics
• Ab initio results for the broken phase of scalar light front field theory
• Can DLCQ test the Maldacena Conjecture?
• SDLCQ: Supersymmetric Discrete Light Cone Quantization
• Application of Pauli-Villars Regularization and Discretized Light-Cone Quantization to a (3+1)-Dimensional Model
• On the nonperturbative solution of Pauli--Villars-regulated light-front QED: A comparison of the sector-dependent and standard parameterizations
• Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory
• A transition in the spectrum of the topological sector of ${\varphi }_2^4$ theory at strong coupling
• The stability of the scalar ${\chi }^2\varphi$ interaction
• Generalized parton distributions in a light-front nonperturbative approach
• The mass renormalization of nonperturbative light-front Hamiltonian theory: An illustration using truncated, Pauli-Villars-regulated Yukawa interactions
• Direct evidence for the Maldacena conjecture for N=(8,8) super Yang-Mills theory in 1+1 dimensions
• A nonperturbative calculation of the electron's magnetic moment with truncation extended to two photons
• Relativistic bound states in Yukawa model
• Nonperturbative renormalization in a scalar model within Light-Front Dynamics
• Ground states of the Wick-Cutkosky model using light-front dynamics
• Wave functions and properties of massive states in three-dimensional supersymmetric Yang-Mills theory
• The Mass Spectrum of N=1 SYM(2+1) at Strong Coupling
• Renormalized nonperturbative fermion model in Covariant Light Front Dynamics
• N=(1,1) Super Yang-Mills on a (2+1) Dimensional Transverse Lattice with one Exact Supersymmetry
• Restoration of rotational invariance of bound states on the light front
• Two-boson truncation of Pauli-Villars-regulated Yukawa theory
• Coherent States in Null-Plane Q.E.D
• Regularization of fermion self-energy and electromagnetic vertex in Yukawa model within light-front dynamics
• $k^{+}=0$ Modes in Light-Cone Quantization
• Nonperturbative Pauli-Villars regularization of vacuum polarization in light-front QED
• Application of the light-front coupled-cluster method to ${\varphi }^4$ theory in two dimensions
• Exact solutions to Pauli-Villars-regulated field theories
• Advances in Basis Light-front Quantization
• Phase Transition in Light-Front ${\varphi }_{1+1}^4$
• A first nonperturbative calculation in light-front QED for an arbitrary covariant gauge
• On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation
• Basis of symmetric polynomials for many-boson light-front wave functions
• QED(1+1) at Finite Temperature -- a Study with Light-Cone Quantisation
• Restoration of the chiral limit in Pauli-Villars-regulated light-front QED
• The Lamb Shift in a Light Front Hamiltonian Approach
• Mesonic Spectrum of Two Dimensional Supersymmetric Theories
• Light-Front QCD(1+1) Coupled to Chiral Adjoint Fermions
• Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization
• Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED
• Renormalization group procedure for effective particles: elementary example of exact solution with finite mass corrections and no involvement of vacuum
• Spectrum and thermodynamic properties of two-dimensional N=(1,1) super Yang-Mills theory with fundamental matter and a Chern-Simons term
• The sine-Gordon model and the small k^+ region of light-cone perturbation theory
• The Continuum Version of ϕ^4_{1+1}-theory in Light-Front Quantization
• Symmetric multivariate polynomials as a basis for three-boson light-front wave functions
• The Light-Front Vacuum
• Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD
• Infra-red Divergences in Light-Front QED and Coherent State Basis
• The box diagram in Yukawa theory
• Two-Point Stress-Tensor Correlator in N=1 SYM(2+1)
• N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature
• Deuteron binding energies and form factors from light front field theory
• Light front QED${}_{1+1}$ at finite temperature
• Broken phase of the O(N) ϕ^4 model in light cone quantization and 1/N expansion
• Theta-Vacuum of the Bosonized Massive Light-Front Schwinger Model
• Spontaneous symmetry breaking in light front field theory
• Dynamics on the Light Cone : Compact versus Continuum Quantization
• Mesons in Light-Front QCD${}_{2+1}$: Investigation of a Bloch Effective Hamiltonian
• Effects of Massive Gluons on Quarkonia in Light-Front QCD
• Light-cone zero modes revisited
• Fermionic Zero Modes and Spontaneous Symmetry Breaking on the Light Front
• Critical properties of ${\Phi }_{1+1}^4$-theory in Light-Cone Quantization
• Fermion mass mixing and vacuum triviality in the renormalization group procedure for effective particles
• Anomalously light mesons in a (1+1)-dimensional supersymmetric theory with fundamental matter
• Systematic Renormalization in Hamiltonian Light-Front Field Theory
• Light-front Nambu--Jona-Lasinio model at finite temperature and density
• Anomalously light states in super-Yang-Mills Chern-Simons theory
• Simulation of Dimensionally Reduced SYM-Chern-Simons Theory
• Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
• Fermions on the light front transverse lattice
• Quantum Electrodynamics at strong Couplings
• Light-Front Dynamic Analysis of Bound States in Scalar Field Model
• Properties of the Bound States of Super-Yang-Mills-Chern-Simons Theory
• Does DLCQ S-matrix have a covariant continuum limit?
• Approximate BPS states
• Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization
• Decoupling of Zero-Modes and Covariance in the Light-Front Formulation of Supersymmetric Theories
• Generalized BRST Quantization and Massive Vector Fields
• Spectrum of N=1 massive super Yang-Mills theory with fundamental matter in 1+1 dimensions
• The Casimir Effect on the Light-Cone
• Hamiltonian Formulations of Yang-Mills Quantum Theory and the Gribov Problem
• Cancellation of Infrared divergences to all orders in LFQED
• Spontaneously broken quark helicity symmetry
• Two-dimensional super Yang-Mills theory investigated with improved resolution
• An application of the light-front coupled-cluster method to the nonperturbative solution of QED
• Renormalizing DLCQ Using Supersymmetry
• Linked-cluster Tamm-Dancoff Field Theory
• Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach
• Light-front analysis of the Casimir effect
• Higgs mechanism in a light front formulation
• BRST-invariant Pauli-Villars regularization of QCD
• Hamiltonian Approach to the Gribov Problem

Cited by in corpus (35)

• 50 Years of Quantum Chromodynamics
• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• Quarkonium as relativistic bound state on the light front
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Lattice Renormalization of Quantum Simulations
• Lightcone Effective Hamiltonians and RG Flows
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Frame dependence of form factors in light-front dynamics
• The non-triviality of the vacuum in light-front quantization: An elementary treatment
• Light-front wavefunctions of mesons by design
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• Distribution amplitudes of light diquarks
• Theory introduction to baryon spectroscopy
• Three-body model for $K(1460)$ resonance
• Hadron Spectra, Decays and Scattering Properties within Basis Light Front Quantization
• Trends and Progress in Nuclear and Hadron Physics: a straight or winding road
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Basis Light-Front Quantization for a Chiral Nucleon-Pion Lagrangian
• Gravitational form factor $D$ of charmonium from shear stress
• Stress out of charmonia
• Light-front ${\varphi }_2^4$ theory with sector-dependent mass
• Computation of effective front form Hamiltonians for massive Abelian gauge theory
• Coulomb- quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex
• Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory
• Tadpoles and vacuum bubbles in light-front quantization
• Dissecting a strongly coupled scalar nucleon
• Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory
• Flavor asymmetry from the non-perturbative nucleon sea
• Nucleon Structure from Basis Light-Front Quantization : Status and Prospects
• Symmetry breaking in light-front ${\varphi }^4$ theory
• Simulating quantum field theories on gate-based quantum computers
• Covariant analysis of electromagnetic current on the light cone: exposition with scalar Yukawa theory
• Convergence of the light-front coupled-cluster method in quenched scalar Yukawa theory
• Casimir force on a light front
• Quantum entanglement between partons in a strongly coupled quantum field theory