arXiv subjects

Jorge G. Cardoso

Publications and source records attributed to Jorge G. Cardoso.

3 recordsLinked to original sources

arXiv2026

Spin Curvatures in General Relativity and Two-Component Gravitons with Arbitrary Sources

We present a short review of the spin curvatures that arise within the framework of one of the Infeld-van der Waerden formalisms for general relativity. All the spinor symmetries borne by the inner structure of general relativity are thus exhibited in an explicit way. The sourceful extension formulated in an earlier work of the two-component theory of gravitons in vacuum is concisely reviewed in connection with the establishment of an important total-symmetry property related to the energy-momentum conservation law of general relativity.

gr-qc↗

arXiv2016

The Classical World and Spinor Formalisms of General Relativity

A review of some facts concerning classical spacetime geometry is presented together with a description of the most elementary aspects of the two-component spinor formalisms of Infeld and van der Waerden. Special attention is concentrated upon the gauge characterization of the basic geometric objects borne by the formalisms. It is pointed out that spin-affine configurations are most naively defined by carrying out parallel displacements of null world vectors within the framework of the γ-formalism. The standard result that assigns a covariant gauge behaviour to the symmetric parts of any admissible spin connexions is deduced out of building up a generalized version of spin transformation laws. A fairly complete algebraic description of curvature splittings is carried out on the basis of the construction of a set of spinor commutators for each formalism. The pertinent computations take up the utilization of some covariant differential prescriptions which facilitate specifying the action of the commutators on arbitrary spin tensors and densities. It turns out that the implementation of such commutators under certain circumstances gives rise to a system of wave equations for gravitons and Infeld-van der Waerden photons which possess in either formalism a gauge-invariance property associated with appropriate spinor-index configurations. The situation regarding the accomplishment of the couplings between Dirac fields and electromagnetic curvatures is entertained to a considerable extent.

math-ph↗

arXiv2012

Pseudo-Unitary Dynamics of Free Relativistic Quantum Mechanical Twofold Systems

A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably normalized vectors belonging to the two-complex-dimensional spaces that occur in local orthogonal decompositions of isomorphic copies of Cartan's space. The corresponding dynamical variables thus show up as bounded pseudo-Hermitian operator restrictions that possess real discrete spectra. Any measurement processes have to be performed locally in orthocronous proper Lorentz frames, but typical observational correlations are expressed in terms of symbolic configurations which come from the covariant action on spaces of state vectors of the Poincaré subgroup of an adequate realization of SU(2,2). The overall approach turns out to supply a supposedly natural description of the dynamics of free twofold systems in flat spacetime. One of the main outlooks devised here brings forward the possibility of carrying out methodically the construction of a background to a new relativistic theory of quantum information.

math-ph↗