Paul BaldufThe present article describes the package "Lips" (short for "Lorentz invariant phase space"), whose primary purpose is to generate valid sets of momenta for scattering amplitudes: A scattering amplitude is a function of masses and momenta of a set of particles, and it usually implies various constraints to these (e.g. masses should be positive, momenta should be conserved, individual momenta should square to given values, etc.). This makes it a non-trivial task to produce concrete numerical values of momenta that satisfy these constraints. Beyond that, one might also require specific types of numbers (rational, complex, p-adic, etc), or represent the momenta as spinors. The package can also do further calculations that arise in this context, such as evaluating spin-helicity expressions.
https://arxiv.org/abs/2305.14075
Lips: p-adic and singular phase space
I present new features of the open-source Python package lips, which leverages the newly developed pyadic and syngular libraries. These developments enable the generation and manipulation of massless phase-space configurations beyond real kinematics, defined in terms of four-momenta or Weyl spinors, not only over complex numbers ($\mathbb{C}$), but now also over finite fields ($\mathbb{F}_p$) and p-adic numbers ($\mathbb{Q}_p$). The package also offers tools to evaluate arbitrary spinor-helicity expressions in any of these fields. Furthermore, using the algebraic-geometry submodule, which utilizes Singular [1] through the Python interface syngular, one can define and manipulate ideals in spinor variables, enabling the identification of irreducible surfaces where scattering amplitudes have well-defined zeros and poles. As an example application, I demonstrate how to infer valid partial-fraction decompositions from numerical evaluations.
Ben Fulton
Center for Open Science
Kemal
Kohulan Rajan
Jeremy Monat
Christian Meesters
Daniel Huppmann
