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.

611 Electrons propagating through the bidimensional structure of graphene have a linear relation between energy and momentum, and thus behave as massless Dirac fermions1–3. Consequently, graphene exhibits electronic properties for a two-dimensional (2D) gas of charged particles described by the relativistic Dirac equation, rather than the non-relativistic Schrödinger equation with an eff ective...

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The Schrödinger and Klein–Gordon equations are demonstrated as geodesic equations in this framework. A development of the intrinsic properties of this theory, using t...

The non-minimal coupling of fermions to a background responsible for the breaking of Lorentz symmetry is introduced in Dirac’s equation; the non-relativistic regime is contemplated, and the Pauli’s equation is used to to show how an Aharonov-Casher phase appears as a natural consequence of the Lorentz-violating term. Different ways of realizing the Lorentz breaking are presented and, in each ca...

Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schrödinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC ...

We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial torsion fields. The consistent hydrodynamical formulation is constructed for quantum system Dirac fermions on basis nonrelativistic Pauli-like equation obtained via Foldy–Wouthuysen transformation. With help Madelung decomposition approach,...

Certain of Takabayasi's criticisms of a causal re·interpretation of the quantum theory are answered in detail. It is indicated .how this interpretation can be extended to the Dirac equation, and the problem of the identity of equivalent particles is discussed, for the case of particles that satisfy the Pauli principle. Possible extensions of theory are indicated. Finally" criticisms at the phil...

The Aharonov-Casher (AC) phase is calculated in relativistic wave equations of spin one. The AC phase has previously been calculated from the Dirac-Pauli equation using a gauge-like technique [1, 2]. In the spin-one case, we use Kemmer theory (a Dirac-like particle theory) to calculate the phase in a similar manner. However the vector formalism, the Proca theory, is more widely known and used. ...

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holo...

OF THE DISSERTATION Connections with Bohmian Mechanics by James Oliver Taylor Dissertation Director: Sheldon Goldstein We begin by formulating non-relativistic Bohmian mechanics for theories in which the wave functions are sections of a Hermitian vector bundle over a Riemannian manifold. We give geometric interpretations of the Pauli equation and the Dirac equation. We then explain the influenc...