Broken Chiral Symmetry on a Null Plane

Understand

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincar\'e generators), while the vacuum state is a chiral invariant.

• This property is used to give a general proof of Goldstone's theorem on a null-plane.
• Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified.
• In particular, the null-plane Gell-Mann-Oakes-Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates.