Light Front Quantization

TL;DR

Light-Front quantization is presented as a physically insightful framework for describing hadron structure and deep inelastic scattering via quark-gluon degrees of freedom. The paper surveys the canonical LF quantization procedure, the peculiar but advantageous LF vacuum (trivial except for zero modes), and the renormalization challenges that arise in a noncovariant setting. It then outlines nonperturbative strategies—Discrete Light-Cone Quantization, transverse lattices with Hamiltonian Monte Carlo, and Light-Front Tamm-Dancoff—to solve bound-state problems, emphasizing how vacuum condensates can be encoded as effective LF interactions. Overall, three main directions for constructing a LF Hamiltonian for QCD are discussed: fundamental zero-mode inclusion, effective zero-mode approaches, and LF-Tamm-Dancoff with renormalization-group constraints, each with its own advantages and outstanding questions.

Abstract

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-Cone Quantization, the transverse lattice and Light-Front Tamm-Dancoff (in combination with renormalization group techniques) are the main tools for exploring LF-Hamiltonians nonperturbatively.

Figures (13)

• Figure 1: Inclusive process $e^-+N \rightarrow e^{-\prime}+X$, where $X$ is an unidentified hadronic state.
• Figure 2: Inclusive lepton nucleon cross section expressed in terms of the imaginary part of the forward Compton amplitude. For $Q^2=-q^2\rightarrow \infty$ only the 'handbag diagram' (both photons couple to the same quark) survives. The 'crossed diagram' (the two photons couple to different quarks) is suppressed because of wavefunction effects.
• Figure 3: Free dispersion relation in $\varepsilon$-coordinates versus the dispersion relation in the LF limit.
• Figure 4: Schematic occupation of modes in the presence of a particle with momentum $p_-$ for $\varepsilon/L \ll 1$ (i.e. "close to the LF"). The modes near $k_-=0$ are already present in the vacuum and are dynamically restricted to $k_- = {\cal O} \left( m (\varepsilon /L)^{(1/2)}\right)$ The "parton distribution", i.e. the modes which are occupied in the presence of the particle but not in the vacuum, vanish at small $k_-$ at a momentum scale which remains finite as $\varepsilon /L\rightarrow 0$. The presence of the cutoffs has almost no effect on the dynamics.
• Figure 5: ${\cal O}(\lambda^2)$-corrections to the mode density in the presence of a particle with momentum $P$. a.) disconnected corrections, b.) insertions into generalized tadpoles (i.e. diagrams where a subgraph is connected with the rest of the diagram at one point only) and c.) non-tadpole connected corrections.