How to get something from nothing: null state, bootstrap and Dyson-Schwinger

Abstract

I will start with a brief overview of the 2D minimial model CFTs, the first successful examples of the conformal bootstrap program. The null state condition for the minimal models can be viewed as a quantization condition for these strongly coupled systems. I want to explain that the null state condition can be applied to a broader context, i.e. without assuming conformal symmetry. I will discuss the use of the null state condition in the quantum mechanical bootstrap in both the Hamiltonian and Lagrangian formalisms. In the Lagrangian case, the underdetermined Dyson-Schwinger equations are solved by imposing the null state condition.