RGApproachToInteractingFermions

Introduction

The renormalization group (RG) is a very powerful tool in physics. Essentially, it is a way to continuously map a given theory onto other theories possessing the same low-energy physics by successively integrating out "fast", or high-energy, modes. This is expressed in terms of differential equations giving the "flows" of different coupling constants that appear in the theory.

The basic proceedure is as follows. Let us consider a given interacting Hamiltonian, and write the associated partition function in path integral form:

Failed to parse (syntax error): {\displaystyle Z=\int{D[\psi^{\ast},\psi] e^{-S[\psi^{\ast},\psi]},}

where the action $S$ is