arXiv subjects

J. G. Cardoso

Publications and source records attributed to J. G. Cardoso.

10 recordsLinked to original sources

arXiv2026

A Pseudo-Unitary Version of Schwinger's Symbolism of Atomic Measurements and a Prospect for a New Relativistic Quantum Information Theory

The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincaré subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schrödinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.

quant-ph↗

arXiv2025

Geometry of Curved Spacetimes Equipped with Torsionful Affinities and Einstein-Cartan's Theory in Two-Component Spinor Form

The classical world structures borne by spacetimes endowed with torsionful affinities are reviewed. Subsequently, the definition and symmetry properties of a typical pair of Witten curvature spinors for such spacetimes are exhibited along with a comprehensive two-component spinor transcription of Einstein-Cartan's theory. A full description of the correspondence principle that interrelates Einstein-Cartan's theory and general relativity is likewise presented.

gr-qc↗

arXiv2025

On the Weyl Tensor for a Curved Spacetime Endowed with a Torsionful Affinity

We transcribe into the framework of the torsionful version of the ε-formalism of Infeld and van der Waerden the world definition of the Weyl tensor for a curved spacetime that occurs in the realm of Einstein-Cartan's theory. The resulting expression shows us that it is not possible to attain any general condition for conformal flatness in such a spacetime even if wave functions for gravitons are eventually taken to vanish identically. A short discussion on the situation concerning the limiting case of general relativity is presented thereafter.

gr-qc↗

arXiv2023

A Torsional Two-Component Description of the Motion of Dirac Particles at Early Stages of the Cosmic Evolution

It is assumed that the non-singular big-bang birth of the Universe as set forth by Einstein-Cartan's theory particularly brought about the appearance of the cosmic microwave and dark energy backgrounds, dark matter, gravitons as well as of Dirac particles. On account of this assumption, a two-component description of the motion of quarks and leptons prior to the occurrence of hadronization is presented within the framework of the torsionful ε-formalism of Infeld and van der Waerden. The relevant field equations are settled on the basis of the implementation of conjugate minimal coupling covariant derivative operators that carry additively typical potentials for the cosmic backgrounds such as geometrically specified in a previous work. It appears that the derivation of the wave equations which control the spacetime propagation of Dirac fields at very early stages of the cosmic evolution, must be tied up with the applicability of certain subsidiary relations. The wave equations themselves suggest that quarks and leptons interact not only with both of the cosmic backgrounds, but also with dark matter. Nevertheless, it becomes manifest that the inner structure of the framework allowed for does not give rise at all to any interaction between gravitons and Dirac particles. The overall formulation ascribes an intrinsically non-geometric character to Dirac's theory, in addition to exhibiting a formal evidence that dark energy and dark matter must have partaken of a cosmic process of hadronization.

gr-qc↗

arXiv2023

The non-singular Trautman-Kopczyński big-bang model and a torsional spinor description of dark matter

A view is taken up whereby the non-singular Trautman-Kopczyński big-bang creation of the Universe produced a highly torsional hot state at early stages of the cosmic evolution which particularly brought about the formation of a dark matter cloud. It is thus assumed that the combination of Einstein-Cartan's theory with the torsionful version of the two-component ε-formalism of Infeld and van der Waerden supplies a natural local description of dark matter in terms of uncharged spin-one massive fields. In the case of either handedness, the pertinent spinor field equation arises directly from a suitable form of the world Bianchi identity. It appears that each such field equation bears a term that is thought of as carrying part of the information on the mass of the fields. The whole information turns out to be extracted by well prescribed derivatives of certain couplings involving the fields and spinor torsion pieces in such a way that the mass of dark matter is really thought of as arising from the interaction between the fields and spinor torsion.

gr-qc↗

arXiv2022

Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are carried by the wave equations at issue. What results is, in effect, that the only interactions which ultimately occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.

gr-qc↗

arXiv2016

A Local Description of Dark Energy in Terms of Classical Two-Component Massive Spin-One Uncharged Fields on Spacetimes with Torsionful Affinities

It is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deriving explicitly the wave equations that supposedly control the propagation in spacetime of the dark energy background. What immediately comes out of this derivation is a presumably natural display of interactions between the fields and both spin torsion and curvatures. The physical properties that may arise directly from the solutions to the wave equations are not brought out.

gr-qc↗

arXiv2015

Two-Component Spinors in Spacetimes with Torsionful Affinities

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by the traditional formalisms. Any spin-affine connexion appears to possess a torsional part which is conveniently chosen as a suitable asymmetric contribution. Such a torsional affine contribution thus supplies a gauge-invariant potential that can eventually be taken to carry an observable character, and thereby effectively takes over the role of any trivially realizable symmetric contribution. The overall curvature spinors for any spin-affine connexion accordingly emerge from the irreducible decomposition of a mixed world-spin object which in turn comes out of the action on elementary spinors of a typical torsionful second-order covariant derivative operator. Explicit curvature expansions are likewise exhibited which fill in the gap related to their absence from the literature. It is then pointed out that the utilization of the torsionful spinor framework may afford locally some new physical descriptions.

math-ph↗

arXiv2013

Absence of Differential Correlations Between the Wave Equations for Upper-Lower One-Index Twistor Fields Borne by the Infeld-van der Waerden Spinor Formalisms for General Relativity

It is pointed out that the wave equations for any upper-lower one-index twistor fields which take place in the frameworks of the Infeld-van der Waerden γε-formalisms must be formally the same. The only reason for the occurrence of this result seems to be directly related to the fact that the spinor translation of the traditional conformal Killing equation yields twistor equations of the same form. It thus appears that the conventional torsionless devices for keeping track in the γ-formalism of valences of spinor differential configurations turn out not to be useful for sorting out the typical patterns of the equations at issue.

math-ph↗

arXiv2010

Wave Equations for Invariant Infeld-van der Waerden Wave Functions for Photons and Their Physical Significance

The inner structure of the γε-formalisms of Infeld and van der Waerden admits the occurrence of spin-tensor electromagnetic fields which bear invariance under the action of the generalized Weyl gauge group. A concise derivation of the wave equations for such fields is carried out explicitly along with the construction of a set of torsionless covariant-derivative expressions. It is emphatically pointed out that the integration of the wave equations arising herein may under certain circumstances produce significant insights into the situation concerning the description of some physical properties of the cosmic microwave background.

math-ph↗