On-shell gauge invariant three-point amplitudes
A bstract 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 wit...
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Veröffentlicht in: | The journal of high energy physics 2017-12, Vol.2017 (12), p.1-26, Article 48 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A
bstract
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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ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP12(2017)048 |