Torsion Field Research Articles

Formula omitted] mechanics of general [formula omitted] multiplets

We construct the manifestly N = 4 supersymmetric off-shell superfield “master” action for any number n of the N = 4 supermultiplets ( 4 , 4 , 0 ) described by harmonic analytic superfields q + a ( ζ , u ) , a = 1 , … , 2 n , subjected to the most general harmonic constraints. The action consists of the sigma-model and Wess–Zumino parts. We present the general expressions for the target space metric, torsion and background gauge fields. The generic target space geometry is shown to be weak HKT (hyper-Kähler with torsion), with the strong HKT and HK ones as particular cases. The background gauge fields obey the self-duality condition. Our formulation suggests that the weak HKT geometry is fully specified by the two primary potentials: an unconstrained scalar potential L ( q + , q − , u ) | θ = 0 which is the θ = 0 projection of the superfield sigma-model Lagrangian, and a charge 3 harmonic analytic potential L + 3 a ( q + , u ) | θ = 0 coming from the harmonic constraint on q + a . The reductions to the strong HKT and HK geometries amount to simple restrictions on the underlying potentials. We also show, using the N = 2 superfield approach, that the most general bosonic target geometry of the N = 4 , d = 1 sigma models, of which the weak HKT geometry is a particular case, naturally comes out after adding the mirror ( 4 , 4 , 0 ) multiplets with different transformation laws under N = 4 supersymmetry and SO ( 4 ) R symmetry. Thus the minimal dimension of the target spaces exhibiting such a “weakest” geometry is 8, which corresponds to a pair of the mutually mirror ( 4 , 4 , 0 ) multiplets.

Fermion confinement induced by geometry

We consider a five-dimensional model in which fermions are confined in a hypersurface due to an interaction with a purely geometric field. Inspired by the Rubakov-Shaposhnikov field-theoretical model, in which massless fermions can be localized in a domain wall through the interaction of a scalar field, we show that particle confinement may also take place if we endow the five-dimensional bulk with a Weyl integrable geometric structure, or if we assume the existence of a torsion field acting in the bulk. In this picture, the kind of interaction considered in the Rubakov-Shaposhnikov model is replaced by the interaction of fermions with a geometric field, namely a Weyl scalar field or a torsion field. We show that in both cases the confinement is independent of the energy and the mass of the fermionic particle. We generalize these results to the case in which the bulk is an arbitrary n-dimensional curved space.

Constraining spacetime torsion with the Moon and Mercury

We report a search for new gravitational physics phenomena based on Riemann-Cartan theory of general relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth, and Cabi, we analyze the motion of test bodies in the presence of torsion, and, in particular, we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We consider the motion of a test body in a spherically symmetric field, and the motion of a satellite in the gravitational field of the Sun and the Earth. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general differ from geodesics when torsion is present. We derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of celestial mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter of the satellite. The computed secular variations show how the corrections to the perihelion advance and to the orbital de Sitter effect depend on the torsion parameters. All computations are performed under the assumptions of weak field and slow motion. To test our predictions, we use the measurements of the Moon's geodetic precession from lunar laser ranging data, and the measurements of Mercury's perihelion advance from planetary radar ranging data. These measurements are then used to constrain suitable linear combinations of the torsion parameters.

Constraints on torsion from the bosonic sector of Lorentz violation and magnetogenesis data

A. Kostelecky et al. [Phys. Rev. Lett. 100 (2008) 111102], have shown that there is an exceptional sensitivity of spacetime torsion components by coupling it to fermions and constraining it to Lorentz violation. They obtain new constraints on torsion components down to the level of 10 − 31 GeV . Yet more recently, L.C. Garcia de Andrade [Phys. Lett. B 468 (2011) 28] has shown that the photon sector of Lorentz violation (LV) Lagrangian leads to linear non-standard Maxwell equations where the magnetic field decays slower giving rise to a seed for galactic dynamos. In this paper bounds are placed on torsion based on the magnetogenesis or the origin of magnetic fields in the universe. On a coherence scale of 10 kpc, galactic magnetic fields of the order of some μG yield a torsion primordial field of the order of K 0 ≈ 10 − 48 GeV . Just to give an idea of how tiny it is we mention that torsion limit in the Early universe yield K 0 ≈ 10 − 31 GeV had been obtained by V. de Sabbata and C. Sivaram. Good limits were also obtained by B.R. Heckel et al. [Phys. Rev. D 78 (2008) 092006]. In our case the advantage from astro-particle physics point of view, is that a very small seed torsion field is enough to seed galactic dynamo. C. Sivaram limit is obtained from a massive photon electrodynamics [L.C. Garcia de Andrade, C. Sivaram, Ap. Space Sci. 209 (1993) 109] where a gauge invariant electrodynamics is used. Dynamo stars data are able to raise this value of torsion up to 10 − 34 GeV at magnetar atmosphere. From these estimates one notices that they coincide with the ones obtained by A. Kostelecky et al., the difference being basically in the method. The ones here were obtained from magnetogenesis data while theirs were obtained from the Earth laboratory data from polarised electrons. Besides here one used the torsion derivatives while A. Kostelecky et al. uses the constant axial torsion tensor. Another fundamental distinction is that we use bosonic sector of the Lagrangian while they use mainly fermionic sector coupling with torsion.

THE EMBEDDING OF THE SPACETIME IN HIGHER-DIMENSIONAL RIEMANN–CARTAN MANIFOLDS AND CLASSICAL CONFINEMENT OF TEST PARTICLES

We revisit the Riemann–Cartan geometry in the context of recent higher-dimensional theories of spacetime. After introducing the concept of torsion in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Riemann–Cartan geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a bulk with torsion. As an application of this result, we discuss the problem of classical confinement and the stability of motion of particles and photons in the neighborhood of branes for the case when the bulk has torsion. We illustrate our ideas considering the particular case when the embedding space has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the torsion of the embedding manifold. In this way we construct a classical analogue of quantum confinement inspired in theoretical-field models by replacing a scalar field with a torsion field.

Consequences of Unusual Behaviour in Einstein's Field Equations for Advanced Propulsion Schemes

The notion of faster than light travel, passing through parallel universes, or even going back and forth in time is an interesting scientific issue. These activities are examined within Einstein's field equations from an engineering perspective to potentially create a suitable propulsion system. The evaluation revealed a set of circumstances that may lead to an anomalous gravitational distortion in what is normally referred to as the “vacuum field equation.” This can occur in a near flat space-time continuum without any electric, magnetic or torsion fields when the stressenergy tensor vanishes. The distortion, possibly created by a gravitational vortex, is driven purely by the gravitational tensor. The field equations also imply that unusual consequences may follow if one includes nonlinearities; off-diagonal terms in the gravitational or space-continuum tensors; more detailed boundary condition specifications or by creating systems that enjoy over-unity performance. Depending upon definition of the curvature tensor, this may lead to conditions for travel in a parallel universe, faster than light travel and past/future time travel. The problem is to include such conditions within a suitable propulsor design to explore unknowns within the cosmos.

TORSION CORRECTIONS IN BRANE WORLD GRAVITY

In the frame of brane world theory the effects of torsion fields are examined. Considering a five dimensional Non-Riemannian bulk with a noncompact extra dimension, we derive the modified Einstein field equations in a four dimensional (3-brane) arbitrary manifold embedded in this bulk. The necessary matching conditions are investigated assuming that the torsion in the bulk is continuous. In this context the extrinsic curvature is connected to the matter content restricted to the brane and the torsion components of the bulk. As a final result we observe that the corrections – due to torsion fields – in the modified field equations depend crucially on the embedding that is taken. Therefore, by considering a simple embedding, we develop a cosmological model that describes a flat FLRW embedded in a 5-dimensional de Sitter (or Anti de Sitter) spacetime, where a 5-dimensional cosmological constant emerges from the torsion components of the bulk.

Aspects of Interacting Electromagnetic and Torsion Fields

The interaction energy is studied for the coupling of axial torsion fields with photons in the presence of an external electromagnetic field. To this end, we compute the static quantum potential. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done by considering a mass term for the gauge field, the Coulombic piece disappears leading to a screening phase.

ChemInform Abstract: An ab initio Study of the Geometry and Rotational Barrier of 4- Phenylimidazole.

The molecular design of several synthetic artificial enzymes, which mimic the action of the serine proteaseα-chymotrypsin, incorporates the phenylimidazole molecular fragment to play the role of the His-57 residue in the native enzyme active site. Study of these artificial enzymes by molecular modeling techniques requires accurate torsional force field parameters for the phenylimidazole interring bond. This, in turn, requires accurate characterization of the barrier to rotation around this bond. Previous semiempirical calculations of this rotational barrier have neglected geometry optimization of the molecule at the points along the rotational pathway. The 4-phenylimidazole rotational barrier (5.6 kcal mol−1] presented here was obtained by full ab initio geometry optimization at the 3–21G level at each of the points along the rotational pathway.

Interaction of the 4-rotational gauge field with orbital momentum, gravidiamagnetic effect, and orbital experiment “Gravity Probe B”

The direct interaction of the 4-rotational (Lorentzian) gauge field with the angular orbital momentum of an external field is considered. This interaction appears in a new Poincar\'{e} gauge theory of gravitation, in which tetrads are not true gauge fields, but represent some functions of the translational and 4-rotational gauge fields. The given interaction leads to a new effect: the existence of an electronic orbits precession under the action of an intensive external gravitational field (gravidiamagnetic effect), and also substantiates the existence of the direct interaction of the proper angular momentum of a gyroscope with the torsion field, which theoretically can be generated by the rotational angular momentum of the planet the Earth. The latter interaction can be detected by the experiment Gravity Probe B on the satellite orbit.

Fermion fields in Einstein-Cartan theory and the accelerated-decelerated transition in a primordial universe

The accelerated-decelerated transition in a primordial Universe is investigated by using the dynamics of fermion fields within the context of the Einstein-Cartan theory, where, apart from the curvature, the space-time is also described by a torsion field. The model analyzed here has only a fermion field as a source of the gravitational field. The term associated with the spin of the fermion field plays the role of an inflaton which contributes to an accelerated regime whereas the one related to the fermion mass behaves as a matter field and is responsible for a decelerated regime. Hence, by taking into account the spin of a massive fermion field, it is possible to characterize the transition from an accelerated to a decelerated period of the primordial Universe.

CONFINING POTENTIAL FROM INTERACTING MAGNETIC AND TORSION FIELDS

Adopting the gauge-invariant but path-dependent variables formalism, we study the coupling of torsion fields with photons in the presence of an external background electromagnetic. We explicitly show that, in the case of a constant electric field strength expectation value, the static potential remains Coulombic, while in the case of a constant magnetic field strength expectation value a confining potential is obtained. This result displays a marked qualitative departure from the usual coupling of axionlike particles with photons in the presence of an external magnetic field.

RELATIVISTIC LANDAU–AHARONOV–CASHER QUANTIZATION IN TOPOLOGICAL DEFECT SPACE–TIME

In this paper we study the Landau levels arising within the relativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved space–time background with the presence of a torsion field. We use the Aharonov–Casher effect to couple this neutral particle with the electric field in this curved background. The eigenfunction and eigenvalues of the Hamiltonian are obtained. We show that the presence of the topological defect breaks the infinite degeneracy of the relativistic Landau levels arising in this system. We study the nonrelativistic limit of the eigenvalues and compare these results with cases studied earlier.

Infrared modified gravity with dynamical torsion

We continue the recent study of the possibility of constructing a consistent infrared modification of gravity by treating the vierbein and connection as independent dynamical fields. We present the generalized Fierz-Pauli equation that governs the propagation of a massive spin-2 mode in a model of this sort in the backgrounds of arbitrary torsionless Einstein manifolds. We show explicitly that the number of propagating degrees of freedom in these backgrounds remains the same as in flat space-time. This generalizes the recent result that the Boulware-Deser phenomenon does not occur in de Sitter and anti-de Sitter backgrounds. We find that, at least for weakly curved backgrounds, there are no ghosts in the model. We also discuss the interaction of sources in flat background. It is generally believed that the spinning matter is the only source of torsion. Our flat space study shows that this is not the case. We demonstrate that an ordinary conserved symmetric energy-momentum tensor can also generate torsion fields and thus excite massive spin-2 degrees of freedom.

HIGH ENERGY ASTROPHYSICAL NEUTRINO FLUX AND MODIFIED DISPERSION RELATIONS

Motivated by the interest in searches for violation of CPT invariance, we study its possible effects in the flavor ratios of high-energy neutrinos coming from cosmic accelerators. In particular, we focus on the effect of an energy-independent new physics contribution to the neutrino flavor oscillation phase and explore whether it is observable in future detectors. Such a contribution could be related not only to CPT violation but also to a nonuniversal coupling of neutrinos to a torsion field. We conclude that this extra phase contribution only becomes observable, in the best case, at energies greater than 1016.5 GeV, which is about five orders of magnitude higher than the most energetic cosmological neutrinos to be detected in the near future. Therefore, if these effects are present only in the oscillation phase, they are going to be unobservable, unless a new mechanism or source capable to produce neutrinos of such energy were detected.

Three-dimensional null point reconnection regimes

Recent advances in theory and computational experiments have shown the need to refine the previous categorization of magnetic reconnection at three-dimensional null points—points at which the magnetic field vanishes. We propose here a division into three different types, depending on the nature of the flow near the spine and fan of the null. The spine is an isolated field line which approaches the null (or recedes from it), while the fan is a surface of field lines which recede from it (or approach it). So-called torsional spine reconnection occurs when field lines in the vicinity of the fan rotate, with current becoming concentrated along the spine so that nearby field lines undergo rotational slippage. In torsional fan reconnection field lines near the spine rotate and create a current that is concentrated in the fan with a rotational flux mismatch and rotational slippage. In both of these regimes, the spine and fan are perpendicular and there is no flux transfer across spine or fan. The third regime, called spine-fan reconnection, is the most common in practice and combines elements of the previous spine and fan models. In this case, in response to a generic shearing motion, the null point collapses to form a current sheet that is focused at the null itself, in a sheet that locally spans both the spine and fan. In this regime the spine and fan are no longer perpendicular and there is flux transfer across both of them.

On possible light–torsion mixing in background magnetic field

The interaction of the light with propagating axial torsion fields in the presence of an external magnetic field has been investigated. Axial torsion fields appearing in higher derivative quantum gravity possess two states, with spin one and zero, with different masses. The torsion field with spin-0 state is a ghost that can be removed if its mass is infinite. We investigate the possibility when the light mixes with the torsion fields resulting in the effect of vacuum birefringence and dichroism. The expressions for ellipticity and the rotation of light polarization axis depending on the coupling constant and the external magnetic field have been obtained.

NON-RIEMANNIAN GEOMETRIES AND HIGHER-DIMENSIONAL THEORIES OF SPACETIME

We discuss the role that non-Riemannian geometries might play in the formulation of modern higher-dimensional spacetime theories. Among the vast number of non-Riemannian geometries we consider the two simplest ones: Weyl geometry and Riemann-Cartan geometry. We approach the problem of classical confinement of particles in branes and show how this question may be investigated in the context of the two mentioned geometries. We show that there is a classical analogue of the confinement of fermions induced by a scalar field and the one that might be induced by a Weyl field. In similar fashion we show that the same role may be played by a torsion field.

Interaction fields based on incompatibility tensor in field theory of plasticity-Part I: Theory-

This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.

FERMION DYNAMICS BY INTERNAL AND SPACETIME SYMMETRIES

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.