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We consider two-dimensional Pauli and Dirac operators with a polynomiallyvanishing magnetic field. The main results of the paper provide resolventexpansions of these operators in the vicinity of their thresholds. It is provedthat the nature of these expansions is fully determined by the flux of themagnetic field. The most important novelty of the proof is a comparison betweenthe spatial asymptotics of the zero modes obtained in two different manners.The result of this matching allows to compute explicitly all the singular termsin the associated resolvent expansions. As an application we show how themagnetic field influences the time decay of the associated wave-functionsquantifying thereby the paramagnetic and diamagnetic effects of the spin.

Spectral properties and time decay of the wave functions of Pauli and Dirac operators in dimension two