| Details: |
The standard model of particle physics relies on the framework of quantum field theory (QFT). Several calculations in this framework relies on the use of Feynman diagrams. While calculationally and conceptually powerful, this approach becomes quickly cumbersome beyond the first few leading orders. In fact, some of the founding fathers of quantum theory like Dirac were vocal in their dislike for this approach and disowned this framework. I will talk about an approach called the Bootstrap which was once popular in the 1960s, abandoned in the 1970s, but has come back into fashion over the last decade or so. As an example I will review how one calculates in a manifestly finite manner, without using Feynman diagrams, critical exponents in the so-called epsilon expansion at the Wilson-Fisher fixed point (eg. critical point of water). I will also discuss how century old mathematics relying on the so-called Bieberbach conjecture gives rise to constraints on low energy physics arising from the S-matrix Bootstrap. |