Abstract
Abstract The expansions of tree-level scattering amplitudes for one theory into amplitudes for another theory, which have been studied in recent work, exhibit hidden connections between different theories that are invisible in the traditional Lagrangian formulism of quantum field theory. In this paper, the general expansion of tree Einstein–Maxwell amplitudes into the Kleiss–Kuijf basis of tree Yang–Mills amplitudes has been derived by applying a method based on differential operators. The obtained coefficients are shared by the expansion of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes and the expansion of tree special Yang–Mills scalar amplitudes into tree BS amplitudes, as well the expansion of tree Dirac–Born–Infeld amplitudes into tree non-linear sigma model amplitudes.
Highlights
The expansions of tree-level amplitudes for one theory into amplitudes for another theory, which have been studied in various recent literatures, exhibit hidden connections between different theories that are invisible in traditional Lagrangian formulism of quantum field theory
We demonstrate how to obtain the expansion of tree Einstein-Maxwell theory (EM) amplitudes into KK basis of tree YM amplitudes efficiently by applying proper differential operators in this paper
The coefficients for KK basis in the expansion are shared by the expansion of tree φ4 amplitudes into tree bi-adjoint scalar (BS) amplitudes, the expansion of tree special Yang-Mills-scalar theory (sYMS) amplitudes into tree BS amplitudes, as well the expansion of tree Dirac-Born-Infeld theory (DBI) amplitudes into tree special extended DBI amplitudes, as have been explained in detail
Summary
The modern researches on S-matrix have exhibited remarkable properties of scattering amplitudes that are not evident up on inspecting traditional Feynman rules. Tree amplitudes of other theories can be generated by acting proper differential operators on tree amplitudes of gravity, the connections between amplitudes of different theories can be represented by differential equations With these relations, expansions of tree amplitudes can be arrived via two paths. The current short paper devote to apply the method based on differential operators to tree amplitudes of Einstein-Maxwell theory (EM), φ4 theory, special Yang-Mills-scalar theory (sYMS), as well as Dirac-Born-Infeld theory (DBI). These ingredients serve as backgrounds for the work in this paper.
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