Second-order renormalized Hamiltonian of Yukawa theory

TL;DR

This paper applies the RGPEP method to Yukawa theory, deriving a well-defined, symmetric effective Hamiltonian up to second order, with new computational techniques for higher-order calculations.

Contribution

It introduces a second-order renormalized Hamiltonian for Yukawa theory using RGPEP and develops computational methods for higher-order effective Hamiltonian calculations.

Findings

Effective Hamiltonian is well-defined and symmetric.

Counterterms are determined for renormalization.

Computational techniques for higher-order calculations are proposed.

Abstract

Using the renormalization group procedure for effective particles (RGPEP) we calculate the effective Hamiltonians in the theory of a fermion field coupled to a scalar field via the Yukawa interaction. The theory is renormalized by the addition of counterterms. Necessary counterterms are determined by computing matrix elements of the effective Hamiltonian. All calculations are performed up to the second order in the expansion in powers of the coupling constant. Renormalized effective Hamiltonians are well-defined symmetric forms acting in the Fock space as opposed to the renormalized bare Hamiltonian, which is not well-defined without regularization. We introduce computational techniques that should streamline higher-order calculations and may be of independent interest.