Much ado about nothing: vacuum and renormalization on the light-front

TL;DR

The work analyzes vacuum structure and renormalization in light-front QCD by arguing that the LF vacuum is trivial and that nontrivial vacuum physics is captured by effective LF Hamiltonians with zero modes integrated out. It supports this with a suite of toy models, including the 't Hooft model, self-interacting scalars, Yukawa theories, and a 3+1D chiral-symmetry-breaking model, showing that ET results can be recovered on the LF through appropriate renormalization and counter-terms. A central mechanism is dynamical vertex mass generation, demonstrated by summing infinite LF-time-ordered diagrams to produce finite helicity-flip amplitudes in the chiral limit, with implications for the renormalization of LF Hamiltonians. Together these results argue that LF quantization can yield the correct physics for light-like observables with potentially simpler intuition and computation, while highlighting ongoing challenges in handling longitudinal gauge dynamics and $k^+$ divergences.

Abstract

In the first part of my lectures, I will use the example of deep-inelastic scattering to explain why light-front coordinates play a distinguished role in many high energy scattering experiments. After a brief introduction into the concept of light-front quantization, I will show that the vacuum for any light-front Hamiltonian is trivial, i.e. the same as for non-interacting fields. In the rest of my lectures, I will discuss several toy models in 1+1 and 3+1 dimensions and discuss how effective light-front Hamiltonians resolve the apparent paradox that results from having a trivial light-front vacuum.

Figures (10)

• Figure 1: DIS from a nucleon or nucleus. Only the scattered lepton is measured.
• Figure 2: Using the optical theorem to relate the inclusive electron nucleon cross section to the imaginary part of the forward Compton amplitude.
• Figure 3: Chiral condensate obtained by evaluating Eq. (\ref{['eq:naivesum']}) as a function of the quark mass. For nonzero quark mass, the (infinite) free part has been subtracted. The result agrees for all quark mass with the calculation done using equal time quantization.
• Figure 4: Generalized tadpole (Feynman-) diagram in $\phi^4$ theory.
• Figure 5: Same as Fig. \ref{['fig:phi4']} but as LF-time ordered diagrams. At least one of the vertices has all lines popping out of or disappearing into the vacuum.