Non-minimal coupling and the gyromagnetic factor of spin-1 and higher-spin fields

Abstract

This thesis investigates non-minimal electromagnetic couplings for spin s = 1 and higherspin fields, focusing on the universality of the gyromagnetic factor (g). From the non-relativistic limit of the non-minimal Proca equation up to O(1/m2), where m is the particle’s mass, we derive an effective Hamiltonian, identifying the g-factor (M1), Darwin, spin-orbit, and electric quadrupole (E2) corrections. We show that a generic spin-1 field has g = 1 + a/q, where q is its electric charge and a is the anomalous moment coupling constant, whereas g = 2 arises from the non-Abelian structure of electroweak W± bosons, countering Belinfante’s conjecture (g = 1/s). New physics or internal substructures are parameterized via a dimension-4, E1-generating operator, and dimension-6 operators that modify the electric corrections and generate their magnetic duals, including M2. Finally, dimensional analysis reveals that an arbitrary, anomalous, renormalizable coupling is allowed for elementary bosons in Minkowski space, rendering g arbitrary rather than fixed at 2