Positive Geometries and Differential Forms with Non-Logarithmic Singularities I

Understand

Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models.

• Their unique canonical forms, providing such quantum mechanical observables, are characterised by having only logarithmic singularities along all the boundaries of the positive geometry.
• However, physical observables have logarithmic singularities just for a subset of theories.
• Thus, it becomes crucial to understand whether a similar paradigm can underlie their structure in more general cases.