Light-Front QFT
Quantizing on a null surface reorganizes relativistic dynamics into light-front momentum and Hamiltonian evolution. This chapter connects its useful kinematics to constrained fields, zero modes, Fock-space truncation, and renormalized observables, where the difficult dynamics remains.
Enter this chapter
Section titled “Enter this chapter”Begin with Light-Front Coordinates and Quantization to identify the null coordinates and the generator of evolution.
Topics
Section titled “Topics”- Light-Front Coordinates and Quantization — Defines light-front time and the invariant-mass operator.
- Light-Front Constraints, Zero Modes, and Vacuum Structure — Tracks degrees of freedom omitted by naive positive-momentum counting.
- Light-Front Fock Space, Wavefunctions, and Bound-State Equations — Builds regulated bound-state wavefunctions.
- DLCQ and Basis Light-Front Quantization — Compares longitudinal discretization with smooth basis regulators.
- Light-Front Regulators, Counterterms, and Symmetry Restoration — Restores required operators and symmetry relations under truncation.
- Light-Front Observables and Continuum Validation — Tests physical observables across independent cutoff limits.
How the ideas fit together
Section titled “How the ideas fit together”Positivity of longitudinal momentum simplifies the Fock description, but constrained fields and zero modes do not behave as ordinary positive-momentum oscillators. Discarding them can therefore erase vacuum or symmetry-breaking information rather than prove it absent. A Fock cutoff also modifies the Hamiltonian and current operators together. A converged eigenvalue is insufficient if matrix elements fail covariance or a Ward identity; regulator limits and independent comparisons remain necessary. Brodsky, Pauli, and Pinsky 1998, §§ 2–3.
Where to go next
Section titled “Where to go next”Continue to Hamiltonian Truncation and Variational Methods to define both the retained subspace and the states it omits.