Spacetime: Arena or Reality?

For small values of the mass (in relation to the angular momentum and electric charge), the Kerr-Newman (KN) solution of Einstein equation reduces to a naked singularity of circular shape. By considering the Hawking and Ellis extended interpretation of the KN spacetime, as well as Wheeler's idea of "charge without charge", the non-trivial topological structure of the extended KN spatial section is found to represent gravitational states with half-integral angular momentum. As a consequence, it can be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin emerge from the spacetime geometry. According to this model, therefore, instead of a simple arena, spacetime must have a concrete existence, being responsible -- through its highly non-trivial topological structures -- for the building blocks of (at least some of) the existing matter in the universe.Comment: Chapter in the book "Relativity and the Dimensionality of the World", Springer series "Fundamental Theories of Physics", Vol. 153 (2007). Volume Editor: Vesselin Petko

Kerr-Newman solution as a Dirac particle

For m^2 < a^2 + q^2, with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr--Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown first that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Next, it is shown that due to the topological structure of the extended KN spacetime it does admit states with half-integral angular momentum. This last property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4pi rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.Comment: 19 pages, 6 figures. References added, section 2 enhanced, an appendix and one figure adde

Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, $1$ and $3/2$.Comment: 20 pages, 12 figure

Gravitomagnetic Moments of the Fundamental Fields

The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square--root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.Comment: 8 pages, RevTeX Style, no figures, changed presentation -- now restricted to fields of spin 0, 1/2 and 1 -- some references adde

Non universality of entanglement convertibility

Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that present phase transitions of different orders. For this purpose, we evaluate the local convertibility between bipartite ground states. Our results suggest that the operational properties, related to non-analyticities of the entanglement spectrum, are good detectors of explicit symmetries of the model, but not necessarily of phase transitions. We also show that thermodynamically equivalent phases, such as Luttinger liquids, may display different convertibility properties depending on the underlying microscopic model.Comment: 5 pages + references, 4 figures - improved versio

Magnetically-controlled impurities in quantum wires with strong Rashba coupling

We investigate the effect of strong spin-orbit interaction on the electronic transport through non-magnetic impurities in one-dimensional systems. When a perpendicular magnetic field is applied, the electron spin polarization becomes momentum-dependent and spin-flip scattering appears, to first order in the applied field, in addition to the usual potential scattering. We analyze a situation in which, by tuning the Fermi level and the Rashba coupling, the magnetic field can suppress the potential scattering. This mechanism should give rise to a significant negative magnetoresistance in the limit of large barriers.Comment: 4 pages, 2 figure