Gyromagnetic ratio ($\gamma$)

The proportionality coefficient between a system's magnetic dipole moment and angular momentum when $\mathbf{\mu }=\gamma \mathbf{J}$ applies. In the angular convention, $\gamma$ is expressed in radians per second per tesla; $\gamma /(2\pi )$ is the corresponding coefficient in cycles per second per tesla. Its sign determines the relative orientations of the magnetic dipole moment and angular momentum.

The magnetic spectra of a scalar field and the Dirac equation do not fix every higher-spin spectrum. In SI units, a charged mode with a specified gyromagnetic ratio corresponding to $g=2$ has the model branchesHere $n=0,1,\dots$ is the Landau level index and $m_s$ is the dimensionless spin projection measured along $q\mathbf{B}$. The power $c^2$ in the magnetic term follows because $|q|\hslash B$ has dimensions of squared momentum in SI units; the Gaussian-unit field convention uses a different power of $c$.

For spin one, the aligned $n=0,m_s=1,p_z=0$ branch becomes $E^2=m^2{c}^4-|q|\hslash |B|c^2$. A negative value signals an instability of the assumed background in this model. This extrapolation requires the stated magnetic coupling: spin alone does not determine $g$ for an arbitrary higher-spin field.