S-matrix calculus using effective particles in the Fock space

TL;DR

This paper presents a method for calculating S-matrix elements using effective particles in the Fock space, demonstrating cutoff-independent results through Hamiltonian renormalization techniques.

Contribution

It introduces a Hamiltonian-based approach for S-matrix calculations that remains consistent across different renormalization schemes and cutoff parameters.

Findings

Scattering amplitudes are identical for Hamiltonians with counterterms and effective particles.

Results are independent of ultraviolet cutoff and renormalization-group parameter.

The method ensures consistent S-matrix calculations in quantum field theory.

Abstract

This article describes a method for calculating S-matrix elements using Hamiltonians obtained in the renormalization group procedure for effective particles. It is shown that the scattering amplitudes obtained using a canonical Hamiltonian $H^\Delta$ with counterterms are the same as those obtained using a renormalized Hamiltonian for effective particles, $H_\lambda$. The result is independent of the ultraviolet cutoff $\Delta$ and the renormalization-group parameter $\lambda$.