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.
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ArXiv ePrint: 1705.08835
First authors (Zhengdi Sun, Hui Xu).
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Sun, Z., Xu, H. & Cheung, YK.E. On-shell gauge invariant three-point amplitudes. J. High Energ. Phys. 2017, 48 (2017). https://doi.org/10.1007/JHEP12(2017)048
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DOI: https://doi.org/10.1007/JHEP12(2017)048