Spinor-helicity three-point amplitudes from local cubic interactions

Abstract

Abstract:We make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions. Both the cubic interactions and the on-shell three-point amplitudes had been independently classified in the literature, but their relation has not been made explicit. The aim of this note is to provide such a relation and discuss similarities and differences of their constructions. For the completeness of our analysis, we also derive the covariant form of all parity-odd massless vertices.

Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes

“…The full list of such vertices can be found in [7]. The possibility of interaction terms like these has also been noted in a recent paper [2]. Normally they would not be considered as proper interactions as PP /Γ is the sum of the free Hamiltonians.…”

“…Based on systematisation and extension of the results of that paper -done in [7] and [8] -the present paper offers a first step in the study of the general quartic vertex operator. 2 As regards the contents of the Metsaev papers, there are two main results (apart from a formal solution for the quartic interaction itself): first, that there are quartic vertices that are Poincaré invariant by themselves independently of the cubic vertices. Second, that the coefficients for the cubic vertices are determined to have a certain form by Poincaré invariance at the quartic level.…”

“…The constructibility assumption -in the sense that quartic amplitudes can be reconstructed from the cubic interaction vertices only -made in BCFW derivations of the quartic higher spin amplitude [10,11] (for a review from a light-front perspective, 2 As far as I'm aware of, there are other groups working on this problem at the present time. This is very good and hopefully we will be able to settle the question (through independent but related efforts) about the existence of consistent quartic interactions in the near future.…”

“…The basic questions are: (1) Under what conditions can on-shell quartic tree amplitudes be reconstructed from the cubic amplitudes (constructibility)? (2) Under what conditions can all on-shell higher order tree amplitudes be reconstructed from the cubic…”

“…1 In the early 1990's, R. Metsaev studied quartic interactions for higher spin fields [4,5] in the light-front gauge. As I have been myself interested in that problem for a long time 1 There indeed seems to be a renewed interest in Minkowski space higher spin theory as evidenced for instance by recent work [1][2][3].…”