Single-particle dynamics of the Anderson impurity model in the presence of a
magnetic field H are considered, using a recently developed local moment
approach that encompasses all energy scales, field and interaction strengths.
For strong coupling in particular, the Kondo scaling regime is recovered. Here
the frequency (ω/ωK) and field (H/ωK)
dependence of the resultant universal scaling spectrum is obtained in large
part analytically, and the field-induced destruction of the Kondo resonance
investigated. The scaling spectrum is found to exhibit the slow logarithmic
tails recently shown to dominate the zero-field scaling spectrum. At the
opposite extreme of the Fermi level, it gives asymptotically exact agreement
with results for statics known from the Bethe ansatz. Good agreement is also
found with the frequency and field-dependence of recent numerical
renormalization group calculations. Differential conductance experiments on
quantum dots in the presence of a magnetic field are likewise considered; and
appear to be well accounted for by the theory. Some new exact results for the
problem are also established