New Affine Coherent States based on Elements of Nonrenormalizable Scalar Field Models

TL;DR

This paper introduces a new class of affine coherent states tailored for nonrenormalizable scalar quantum field models, aiming to improve their quantization and continuum limit behavior.

Contribution

It defines and analyzes affine coherent states based on elements of nonrenormalizable scalar field models, advancing the nontrivial quantization approach.

Findings

Affine coherent states are constructed for nonrenormalizable models.

The approach ensures compatibility of affine field operators with the Hamiltonian.

The method facilitates a better continuum limit for scalar quantum fields.

Abstract

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author's approach to nontrivial formulations of such nonrenormalizable models.