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From amplitudes to analytic wavefunctions

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jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThe field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the analytic structure of the wavefunction potentially allows us to establish bounds on physical observables. In this paper we develop an “amplitude representation” for the flat space wavefunction, which allow us to write the flat space wavefunction as an amplitude-like Feynman integral integrated over an energy-fixing kernel. With this representation it is possible to separate the wavefunction into an amplitude part and a subleading part which is less divergent as the total energy goes to zero. In turn the singularities of the wavefunction can be classified into two sets: amplitude-type singularities, which can be mapped to singularities found in amplitudes (including anomalous thresholds), and wavefunction-type singularities, which are unique to the wavefunction. As an example we study several tree level and one loop diagrams for scalars, and explore their singularities in detail.</jats:p>


Acknowledgements: I would like to thank Enrico Pajer, Scott Melville and Santiago Agüí Salcedo for detailed comments for the draft, as well as Guilherme Pimentel, Arthur Lipstein and Miguel R. Correia for valuable discussions. The author is supported by the Croucher Cambridge International Scholarship.


4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

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Journal of High Energy Physics

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Springer Science and Business Media LLC