We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that harmonic functions can be considered as limiting Carleman 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.

2 Poisson geometry and some generalizations 3 2.1 Poisson manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Dirac structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Twisted structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Symplectic leaves and local structure of Poisson manifolds ...

The angular momentum of the physical electron, modelled as a Dirac fermion coupled to the electromagnetic field, is found to be /2, the same as that of a bare Dirac fermion and independent of the size of the electric charge. The coupled Maxwell-Dirac equations

This article is one of squeal papers. For this decade, I have been studying the Dirac operator on a submanifold as a restriction of the Dirac operator in E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and complet...

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in n-dimensional euclidean space E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a con...

The determination of the optimal distribution of the catalytic activity profile, whichmaximizes the catalytic effectiveness, in created unsteady state conditions, is analyzed andtreated numerically for the case of a simple reaction. It was proven that the modulation, of thetemperature and the reactant concentration of the external bulk fluid, leads to a considerableincrease of the catalytic eff...

This article is one of squeal papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and completely ...

The triality properties of Dirac spinors are studied, including a construction of the algebra of (complexified) biquaternion. It is proved that there exists a vector-representation of Dirac spinors. The massive Dirac equation in the vector-representation is actually self-dual. The Dirac’s idea of non-integrable phases is used to study the behavior of massive term.

We define the Dirac-Fock current to hold the current conservation in the momentumdependent Dirac fields, and discuss its effect on the magnetic-moment in the nuclear matter. It is shown that the Dirac-Fock current can largely reduce the magneticmoment even in the isovector case, whose value has been too big due to the small effective mass in the usual relativistic Hartree approximation.

Dirac deformation of Poisson operators of arbitrary rank is considered. The question when Dirac reduction does not destroy linear Poisson pencils is studied. A class of separability preserving Dirac reductions in the corresponding quasi-bi-Hamiltonian systems of Benenti type is discussed. Two examples of such reductions are given. This paper will appear in J. Phys. A: Math. Gen. AMS 2000 Subjec...