Comparative aspects of spin-dependent interaction potentials for spin-1/2 and spin-1 matter fields

TL;DR

This paper compares spin-dependent interaction potentials for spin-1/2 and spin-1 matter fields, analyzing their similarities, differences, and implications for electromagnetic interactions mediated by massive particles.

Contribution

It provides a detailed comparative analysis of spin- and velocity-dependent potentials for spin-1/2 and spin-1 matter currents, including specific cases relevant to massive photon exchange.

Findings

Identifies similarities in potentials for different spins

Highlights peculiarities of spin-1 versus spin-1/2 interactions

Discusses implications for charge and spin relations in particles

Abstract

This paper sets out to establish a comparative study between classes of spin- and velocity-dependent potentials for spin-1/2 and spin-1 matter currents/sources in the non-relativistic regime. Both (neutral massive) scalar and vector particles are considered to mediate the interactions between (pseudo-)scalar sources or (pseudo-)vector currents. Though our discussion is more general, we contemplate specific cases in which our results may describe the electromagnetic interaction with a massive (Proca-type) photon exchanged between two spin-1/2 or two spin-1 carriers. We highlight the similarities and peculiarities of the potentials for the two different types of charged matter and also focus our attention on the comparison between the particular aspects of two different field representations for spin-1 matter particles. We believe that our results may contribute to a further discussion of the relation between charge, spin and extensibility of elementary particles.