  We present dynamical mean field theory (DMFT) results for the local spectral
densities of the one- and two-particle response functions for the infinite
dimensional Hubbard model in a magnetic field. We look at the different regimes
corresponding to half-filling, near half-filling and well away from
half-filling, for intermediate and strong values of the local interaction $U$.
The low energy results are analyzed in terms of quasiparticles with field
dependent parameters. The renormalized parameters are determined by two
different methods, both based on numerical renormalization group (NRG)
calculations, and we find good agreement. Away from half-filling the
quasiparticle weights, $z_\sigma(H)$, differ according to the spin type
$\sigma=\uparrow$ or $\sigma=\downarrow$. Using the renormalized parameters, we
show that DMFT-NRG results for the local longitudinal and transverse dynamic
spin susceptibilities in an arbitrary field can be understood in terms of
repeated scattering of these quasiparticles. We also check Luttinger's theorem
for the Hubbard model and find it to be satisfied in all parameter regimes and
for all values of the magnetic field.
