Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes

Understand

The dynamical commutators of the light-front Poincar\'e algebra yield first order differential equations in the $p^+$ momenta for the interaction vertex operators.

• The homogeneous solution to the equation for the quartic vertex is studied.
• Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed.
• The existence of quartic contact interactions unrelated to cubic interactions by Poincar\'e symmetry indicates that the higher spin S-matrix is not constructible.