IISER MOHALI

Abstract: Positivity lies at the heart of quantum field theory, underpinning familiar principles such as unitarity, causality, and analyticity. At the same time, many of its fundamental observables exhibit remarkable mathematical structures whose mathematical origin is only beginning to be understood. In this talk, I will discuss a new class of hidden positivity structures that emerge in a surprisingly broad range of quantum field theory observables.

These ideas were originally inspired by recent developments in scattering amplitudes and positive geometry, which suggested that unexpectedly simple mathematical structures might underlie even highly complicated quantum field theory observables. I will show how these remarkably simple positivity constraints arise naturally for scalar Feynman integrals and present evidence that they extend far beyond this setting, appearing in scattering amplitudes, effective field theories, cosmological correlators, and several other quantum field theory observables.

Finally, I will discuss how these positivity properties can be exploited to develop new bootstrap constraints, construct efficient methods for the numerical evaluation of multi-loop Feynman integrals, and suggest new directions for exploring the mathematical structure of quantum field theory. Together, these developments illustrate how unexpectedly simple mathematical structures can emerge from some of the most complicated quantities encountered in quantum field theory and hint at a common mathematical language linking seemingly disparate areas, from effective field theories and scattering amplitudes to Feynman integrals and cosmological correlators.