Quantum fields with classical interactions

TL;DR

This paper systematically classifies various free quantum fields and explores their interactions with classical sources and potentials, providing a foundational framework for understanding quantum field interactions with classical backgrounds.

Contribution

It offers a comprehensive categorization of free quantum fields and analyzes their interactions with classical functions, extending the understanding of quantum fields in classical environments.

Findings

Classification of free quantum fields including scalars, vectors, and fermions.

Analysis of interactions between quantum fields and classical sources or potentials.

Framework for studying quantum fields influenced by classical perturbations.

Abstract

We describe basic types of free fields (1) neutral scalar bosons; (2) massive vector bosons; (3) massless vector bosons; (4) charged scalar bosons; (5) Dirac fermions; (6) Majorana fermions. We also consider free field perturbed by a linear or quadratic perturbation involving a classical (c-number) function: (1) neutral scalar bosons interacting with a linear source; (2) neutral scalar bosons interacting with a mass-like perturbation; (3) massive photons interacting with an classical current; (4) massless photons interacting with an classical current. (5) charged scalar bosons interacting with an electromagnetic potential; (6) Dirac fermions interacting with an electromagnetic potential.