Partially reduced formulation of scalar Yukawa model: Poincare-invariance and unitarity

TL;DR

This paper develops a partially reduced scalar Yukawa model ensuring Poincare invariance and unitarity, providing explicit conserved quantities, quantization, and an S-matrix in the first-order approximation.

Contribution

It introduces a novel partially reduced formulation of the scalar Yukawa model that maintains Poincare invariance and unitarity at the quantum level.

Findings

Conserved quantities satisfy Poincare algebra

Explicit S-matrix expression derived and shown to be unitary

Hamiltonian and momentum operators are consistent with Lorentz invariance

Abstract

We consider a scalar Yukawa-like model in the framework of partially reduced quantum field theory. The reduced Lagrangian of the model consists of free scalar field terms and nonlocal current interaction term. Hamiltonian expressions for conserved quantities arose from a Lorentz-invariance of the model in the momentum representation have been found in the first-order approximation with respect to a coupling constant squared. Canonical quantization of the system is performed. It is shown that the obtained conserved quantities and previously founded the Hamiltonian and the momentum of the system satisfy the commutational relations of the Poincare group. The expression for S-matrix in the current approximation is found. Unitarity of this operator is proven by direct calculation.