= Solution
A plausible extension \b[assuming <gyromagnetic ratio> two] is
$$
E^2=m^2c^4+p_z^2c^2+|e|\hbar|B|c(2n+1-2m_s),\qquad m_s=-s,\ldots,s,
$$
where the spin projection is aligned with the charge-field sign. For spin one the lowest aligned mode has $E^2=m^2c^4-|e|\hbar|B|c$ at $p_z=0$. Above $|eB|>m^2c^3/\hbar$, this is negative: <linear time> <evolution> has exponentially growing/decaying modes, signaling an instability of the assumed background.
Spin alone does not fix a <magnetic moment>. The scalar and Dirac examples cannot establish this formula for every higher-spin particle; the stated instability belongs to the specified $g=2$ field model and its regime of applicability. Interactions and backreaction are needed to describe its eventual outcome.
Back to article page
