Carleman estimates and inverse problems for Dirac operators

We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator. M. Salo is supported by the Academy of Finland. L. Tzou is supported by the Doctoral Post-Graduate Scholarship from the Natural Science and Engineering Research Council of Canada. This article was written while L. Tzou was visiting the University of Helsinki and TKK, whose hospitality is gratefully acknowledged. The authors would like to thank András Vasy and Lauri Ylinen for useful comments.