Year: 2017
Type: article
Abstract: Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches. Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field ϕ and an antisymmetric rank-2 tensor field A μν . Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.
Source: Journal of High Energy Physics
Authors: Zhengdi Sun, Hui Xu, Yeuk-Kwan E. Cheung
Institution: Nanjing University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2620265013