The main objective of this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF ) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M =(M, g, ∇, τg, ↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE ) in the case where M is a Lorentzian spacetime (the general case when M is a RCST will be discussed in another publication). To this aim we introduce the Clifford bundle of multivector fields (Cℓ(M, g)) and the left (Cℓ l We also obtain a representation of the DE Cℓ l in the Clifford bundle Cℓ(M, g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψΞ ∈ sec Cℓ(M, g). This means that to each DHSF Ψ ∈ sec Cℓ l Spin e 1,3 (M ) and to each spin frame Ξ ∈ sec P Spin e 1,3 (M ), there is a well-defined sum of even multivector fields ψΞ ∈ sec Cℓ(M, g) (EMFS ) associated with Ψ. Such an EMFS is called a representative of the DHSF on the given spin frame. And, of course, such a EMFS (the representative of the DHSF ) is not a spinor field. With this crucial distinction between a DHSF and its representatives on the Clifford bundle, we provide a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DE Cℓ l and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the electromagnetic gauge invariance and show that only for the DHE such transformations are of the same mathematical nature, thus suggesting a possible link between them. *

We show that vacuum fluctuations of the stress-energy tensor in two-dimensional dilaton gravity lead to a sharp focusing of light cones near the Planck scale, effectively breaking space up into a large number of causally disconnected regions. This phenomenon, called "asymptotic silence" when it occurs in cosmology, might help explain several puzzling features of quantum gravity, including evidence of spontaneous dimensional reduction at short distances. While our analysis focuses on a simplified two-dimensional model, we argue that the qualitative features should still be present in four dimensions.

We present a purely relativistic effect according to which asymmetric oscillations of a quasi-rigid body slow down or accelerate its fall in a gravitational background.

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool, we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot, in general, be translated from one phase to the other.

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By using a nonholonomic moving frame version of the general covariance principle, an active version of the equivalence principle, an analysis of the gravitational coupling prescription of teleparallel gravity is made. It is shown that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity, even in the presence of fermions. An application to the case of a Dirac spinor is made.

The order parameter of the smectic liquid crystal phase is the same as that of a superfluid or superconductor, namely a complex scalar field. We show that the essential difference in boundary conditions between these systems leads to a markedly different topological structure of the defects. Screw and edge defects can be distinguished topologically. This implies an invariant on an edge dislocation loop so that smectic defects can be topologically linked not unlike defects in ordered systems with non-Abelian fundamental groups. Introduction and summaryClassical dynamics is formulated through a collection of sometimes quite complex [1] and often tedious [2] differential equations, a consequence of the implicit smooth structure of time evolution. From this perspective, dynamics connects initial and final states through a homotopy in the configuration space of the system. When that space has closed, non-contractible loops (i.e., an 'interesting' topology), conservation laws ensue and nontrivial winding classes result in topological defects [3,7]. In three-dimensions, defect lines are characterized by the first homotopy group of the ground state manifold (GSM), π 1 (GSM). In particular, when π 1 is non-Abelian, defect loops with homotopy classes α and β are topologically linked, leaving behind a tether in class αβα −1 β −1 whenever they are crossed [4][5][6][7][8]. It follows that the simple superfluid [9] or its gauged cousin, the superconductor [10], should not enjoy topologically tangled defects since their GSM is the circle S 1 with the Abelian fundamental group .Liquid crystals provide a more complex GSM and, for instance, the biaxial nematic [4, 7, 11] is the 'poster child' for non-Abelian defects. In that system, topological defects are characterized by elements of a small but non-Abelian group leading to situations in which the commutator of elements is not the identity. In comparison, the uniaxial nematic, upon which the smectic-A phase is based, is quite different. Its line defects are characterized by  2 and, as a result, all possible commutators yield the identity. The topology of the smectic phase, however, is more subtle-de Gennes drew a strong analogy between the smectic and the superconductor [12]. This powerful analogy led to a better understanding of the distinction between global and local symmetries [13], the prediction of the analog of the Abrikosov phase [10] dubbed the TGB phase [14], and a dizzying number of different results on the critical behaviour of the nematic to smectic-A transition [15][16][17][18]. However, the smectic has both broken translation and rotational symmetry that spoils the standard homotopy description of defects which works perfectly for the superfluid [7,[19][20][21][22]. Not unlike line and point defects in nematics [23,24] the disclinations act upon the dislocations [21] creating ambiguities in free homotopy classes and, in the case of smectics, obstructions to generating the entire homotopy group [22,25]. In the absence of disclinations, the smectic order parameter ...

We present a tomographic scheme, based on spacetime symmetries, for the reconstruction of the internal degrees of freedom of a Dirac spinor. We discuss the circumstances under which the tomographic group can be taken as SU(2), and how this crucially depends on the choice of the gamma matrix representation. A tomographic reconstruction process based on discrete rotations is considered, as well as a continuous alternative.Comment: 9 pages, LaTeX; v2: minor changes, references added. A slightly revised version has been accepted for publication in Phys. Lett.