Abstract
We calculate the spin flip rates for an electron in a homogeneous magnetic field for low excitations ($N\le 5$). Our results apply for all field strengths including those beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. Existing approximations either assume that the electron is in a sufficiently highly excited state such that its orbit can be assumed to be classical or the magnetic field be weak compared to the critical field. The regime of high magnetic field strength and low excitations is therefore poorly covered by them. By comparing our calculations to different approximations, we find that in the high field, low excitation regime the spin flip rates are lower and the equilibrium spin polarization is less pure then one would get by naively applying existing approximations in this regime.
Highlights
A relativistic electron in a homogeneous magnetic fields is one of the oldest solved problems in relativistic quantum mechanics
By comparing our calculations to different approximations, we find that in the high field, low excitation regime the spin flip rates are lower and the equilibrium spin polarization is less pure one would get by naively applying existing approximations in this regime
Because we obtain an equilibrium spin polarization fairly close to one, we plot for readability 2n↑=ðn↑ þ n↓Þ, which is the deviation of the equilibrium spin polarization from unity
Summary
A relativistic electron in a homogeneous magnetic fields is one of the oldest solved problems in relativistic quantum mechanics. A suitable nonperturbative QED theory can be described in the Furry picture [24] through replacing the vacuum electron states by solutions of the Dirac equation in a magnetic field [4,11,25]. The Furry picture has been applied to the electron in a magnetic field to study vacuum birefringence [26,27], energy corrections to the Landau levels [27,28,29], Compton scattering [30] and synchrotron radiation emission [31,32,33,34,35]. We analytically investigate and numerically compute the spin flip rates of low lying Landau levels and compare and contrast these results with both the S&Tand TB&D-approximations
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