Integrating Polchinski's equation by convergent binary tree expansions

Abstract

We give a solution to Polchinski's equation for the Wilsonian effective action in terms of an expansion in binary trees, and prove that this expansion converges in fermionic field theories, provided the fermionic covariance has finite determinant and decay constants. A novel element of the proof are detailed combinatorial estimates for the number of leaf trees associated to binary trees. The method can be used on standard models of fermionic quantum field theory and quantum statistical mechanics.