Hurwitz numbers from Feynman diagrams

Weight Systems from Feynman Diagrams

We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.

Hawking Radiation from Feynman Diagrams

The aim of this letter is to clarify the relationships between Hawking radiation and the scattering of light by matter falling into a black hole. To this end we analyze the S-matrix elements of a model composed of a massive infalling particle (described by a quantized field) and the radiation field. These fields are coupled by current-current interactions and propagate in the Schwarzschild geom...

0 From Finite Sets to Feynman Diagrams

‘Categorification’ is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category of finite sets serves as a categorified version of the set of natural numbers, with disjoint union and Cartesian product playing the role of addition and mul...

Feynman diagrams versus Fermi-gas Feynman emulator

Calculating Transition Amplitudes from Feynman Diagrams

When one thinks of quantum field theory, one’s mind is undoubtedly drawn to Feynman diagrams. The näıve view these diagrams as merely a concise and standardized way of describing collisions and processes. Feynman diagrams, however, encode a great deal of information, for each one corresponds exactly to the probability amplitude of the transition it describes. In other words, it is easily possib...