Torsion Field Research Articles

Torsion discovery potential and its discrimination at CERN LHC

Torsion models constitute a well-known class of extended quantum gravity models. In this paper we study some phenomenological consequences of a torsion field interacting with fermions at LHC. A torsion field could appear as a new heavy state characterized by its mass and couplings to fermions. These new states will form a resonance decaying into difermions, as occurs in many extensions of the standard model, such as models predicting the existence of additional neutral gauge bosons, usually named Z{sup '}. Using the dielectron channel we evaluate the integrated luminosity needed for a 5{sigma} discovery as a function of the torsion mass, for different coupling values. We also calculate the luminosity needed to discriminate, with 95% C.L., the two possible different torsion natures. Finally, we show that the observed signal coming from the torsion field could be distinguished from a signal coming from a new neutral gauge boson, provided there is enough luminosity.

Landau quantization for a neutral particle in the presence of topological defects

In this paper we study the Landau levels in the nonrelativistic 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 or absence of a torsion field. The eigenfunction and eigenvalues of the Hamiltonian are obtained. We show that the presence of the topological defect breaks the infinite degeneracy of the Landau levels arising in this system. We also apply a duality transformation to discuss this same quantization for a dynamics of a neutral particle with a permanent electric dipole moment.

Dark spinors with torsion in cosmology

We solve one of the open problems in Einstein-Cartan theory, namely, we find a natural matter source whose spin angular momentum tensor is compatible with the cosmological principle. We analyze the resulting evolution equations and find that an epoch of accelerated expansion is an attractor. The torsion field quickly decays in that period. Our results are interpreted in the context of the standard model of cosmology.

WZW Orientifolds and Finite Group Cohomology

The simplest orientifolds of the WZW models are obtained by gauging a \({\mathbb{Z}_2}\) symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion \({g\mapsto(\zeta g)^{-1}}\), where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups \({\Gamma=\mathbb{Z}_2\times Z}\) that combine the \({\mathbb{Z}_2}\)-action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups \({\Gamma=\mathbb{Z} _2\times Z}\).

Teleparallel version of the Levi–Civita vacuum solutions and their energy contents

In this paper, we find the teleparallel version of the Levi–Civita metric and obtain tetrad and the torsion fields. The tensor, vector, and the axial-vector parts of the torsion tensor are evaluated. It is found that the vector part lies along the radial direction only while the axial-vector vanishes everywhere because the metric is diagonal. Further, we use the teleparallel version of Moller, Einstein, Landau–Lifshitz, and Bergmann–Thomson prescriptions to find the energy-momentum distribution of this metric and compare the results with those already found in General Relativity (GR). It is worth mentioning here that momentum is constant in both of the theories for all the prescriptions. The energy in teleparallel theory is equal to the corresponding energy in GR only in the Moller prescription for the remaining prescriptions, the energy does not agree in both theories. We also conclude that Moller's energy-momentum distribution is independent of the coupling constant λ in the teleparallel theory.PACS Nos.: 04.20.–q, 04.20.Cv

LORENTZ GAUGE THEORY AND SPINOR INTERACTION

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

PERSONAL PATTERNS FOR LIVE-LINE WORKERS TO MITIGATE THE BIOLOGIC IMPACT

Except the physiological effects the magnetic field of industrial frequency produces biological effects as well, at values much lower, as resulting from some laboratory analyses combined with epidemiological studies. An alternative survey was initiated by the Russian scientists who discovered the torsional field accompanying the electromagnetic fields as being responsible for the biological negative effects. The Ancu Dinca filters, based on organic macromolecules derived from plants, neutralize the negative effects of the magnetic fields by reducing the subtle fields.

Constraining torsion with Gravity Probe B

It is well-entrenched folklore that all torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally, and consider nonstandard torsion theories in which torsion can be generated by macroscopic rotating objects. In the spirit of $\mathrm{\text{action}}=\mathrm{\text{reaction}}$, if a rotating mass like a planet can generate torsion, then a gyroscope would be expected to feel torsion. An experiment with a gyroscope (without nuclear spin) such as Gravity Probe B (GPB) can test theories where this is the case. Using symmetry arguments, we show that to lowest order, any torsion field around a uniformly rotating spherical mass is determined by seven dimensionless parameters. These parameters effectively generalize the parametrized post-Newtonian formalism and provide a concrete framework for further testing Einstein's general theory of relativity (GR). We construct a parametrized Lagrangian that includes both standard torsion-free GR and Hayashi-Shirafuji maximal torsion gravity as special cases. We demonstrate that classic solar system tests rule out the latter and constrain two observable parameters. We show that Gravity Probe B is an ideal experiment for further constraining nonstandard torsion theories, and work out the most general torsion-induced precession of its gyroscope in terms of our torsion parameters.

GEOMETRIC AND EXTENSOR ALGEBRAS AND THE DIFFERENTIAL GEOMETRY OF ARBITRARY MANIFOLDS

We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U ⊂ M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field γ defining a parallelism structure on U ⊂ M, which represents in a well-defined way the action on U of the restriction there of some given connection ∇ defined on M. Also we give a novel and intrinsic presentation (i.e. one that does not depend on a chosen orthonormal moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds of Cartan's connection operator fields are identified, and both appear in the intrinsic Cartan's structure equations satisfied by the Cartan's torsion and curvature extensor fields. We introduce moreover a metrical extensor g in U corresponding to the restriction there of given metric tensor g defined on M and also introduce the concept of a geometric structure(U, γ ,g) for U ⊂ M and study metric compatibility of covariant derivatives induced by the connection extensor γ. This permits the presentation of the concept of gauge (deformed) derivatives which satisfy noticeable properties useful in differential geometry and geometrical theories of the gravitational field. Several derivatives of operators in metric and geometrical structures, like ordinary and covariant Hodge co-derivatives and some duality identities are exhibited.

Can Gravity Probe B usefully constrain torsion gravity theories?

In most theories of gravity involving torsion, the source for torsion is the intrinsic spin of matter. Since the spins of fermions are normally randomly oriented in macroscopic bodies, the amount of torsion generated by macroscopic bodies is normally negligible. However, in a recent paper, Mao et al. (arXiv:gr-qc/0608121) point out that there is a class of theories, including the Hayashi-Shirafuji (1979) theory, in which the angular momentum of macroscopic spinning bodies generates a significant amount of torsion. They further argue that, by the principle of action equals reaction, one would expect the angular momentum of test bodies to couple to a background torsion field, and therefore the precession of the Gravity Probe B gyroscopes should be affected in these theories by the torsion generated by the Earth. We show that in fact the principle of action equals reaction does not apply to these theories, essentially because the torsion is not an independent dynamical degree of freedom. We examine in detail a generalization of the Hayashi-Shirafuji theory suggested by Mao et al. called Einstein-Hayashi-Shirafuji theory. There are a variety of different versions of this theory, depending on the precise form of the coupling to matter chosen for the torsion. We show that, for any coupling to matter that is compatible with the spin transport equation postulated by Mao et al., the theory has either ghosts or an ill-posed initial-value formulation. These theoretical problems can be avoided by specializing the parameters of the theory and in addition choosing the standard minimal coupling to matter of the torsion tensor. This yields a consistent theory, but one in which the action equals reaction principle is violated, and in which the angular momentum of the gyroscopes does not couple to the Earth's torsion field. Thus, the Einstein-Hayashi-Shirafuji theory does not predict a detectable torsion signal for Gravity Probe B. There may be other torsion theories which do.

On the geometry of nonholonomic mechanical systems with vertical distribution

Let (Q,g) be the configuration space of a nonholonomic mechanical system, where g is a Riemannian metric on Q. Suppose the horizontal distribution D on Q admits a vertical distribution D¯, that is D¯ is an integrable complementary (not necessarily orthogonal) distribution to D in TQ. We prove the existence and uniqueness of a linear connection on (Q,g) subject to some conditions on its torsion and on the covariant derivative of g. Then we show that the solutions of the Lagrange-d’Alembert equations are the geodesics of ∇ and vice versa. All the local components of the torsion and curvature tensor fields of ∇ with respect to an adapted frame field are determined. Finally, two examples are given to illustrate the theory we develop in the paper.

Teleparallel version of the stationary axisymmetric solutions and their energy contents

This work contains the teleparallel version of the stationary axisymmetric solutions. We obtain the tetrad and the torsion fields representing these solutions. The tensor, vector and axial-vector parts of the torsion tensor are evaluated. It is found that the axial-vector has component only along $\rho$ and $z$ directions. The three possibilities of the axial vector depending on the metric function $B$ are discussed. The vector related with spin has also been evaluated and the corresponding extra Hamiltonian is furnished. Further, we use the teleparallel version of M$\ddot{o}$ller prescription to find the energy-momentum distribution of the solutions. It is interesting to note that (for $\lambda=1$) energy and momentum densities in teleparallel theory are equal to the corresponding quantities in GR plus an additional quantity in each, which may become equal under certain conditions. Finally, we discuss the two special cases of the stationary axisymmetric solutions.

SECOND ORDER FORMALISM IN POINCARÉ GAUGE THEORY

Changing the set of independent variables of Poincaré gauge theory and considering, in a manner similar to the second-order formalism of general relativity, the Riemannian part of the Lorentz connection as a function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case, the spin density playing the role of the source current in a Yang–Mills type equation for the torsion. The equivalence of the second-order and conventional first-order formalism is established and the corresponding Noether identities are discussed. Finally, a concrete Lagrangian is constructed and by means of a Yasskin-type ansatz, the field equations are reduced to a conventional Einstein–Proca system. Neglecting higher order terms in the spin-tensor, approximate solutions describing the exterior of a spin-polarized neutron star are presented and the possibility of the experimental detection of the torsion fields is briefly discussed.

Torsion Fields, Cartan–Weyl Space–Time and State-Space Quantum Geometries, their Brownian Motions, and the Time Variables

Torsion Fields, Cartan–Weyl Space–Time and State-Space Quantum Geometries, their Brownian Motions, and the Time Variables

Torsion phenomenology at the CERN LHC

We explore the potential of the CERN Large Hadron Collider (LHC) to test the dynamical torsion parameters. The form of the torsion action can be established from the requirements of consistency of effective quantum field theory. The most phenomenologically relevant part of the torsion tensor is dual to a massive axial vector field. This axial vector has geometric nature, that means it does not belong to any representation of the gauge group of the SM extension or GUT theory. At the same time, torsion should interact with all fermions, that opens the way for the phenomenological applications. We demonstrate that LHC collider can establish unique constraints on the interactions between fermions and torsion field considerably exceeding present experimental lower bounds on the torsion couplings and its mass. It is also shown how possible nonuniversal nature of torsion couplings due to the renormalization group running between the Planck and TeV energy scales can be tested via the combined analysis of Drell-Yan and $t\overline{t}$ production processes.

Field equations of massless fields in the new interpretation of the matrix model

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large- N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the B-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.

About a class of metrical N-linear connections on the 2-tangent bundle

In the paper herein we treat some problems concerning the metric structure on the 2-tangent bundle: T2M. We determine the set of all metric semi-symmetric N-linear connections, in the case when the nonlinear connection N is fixed. We prove that the sets: TN of the transformations of N-linear connection having the same nonlinear connections N and msT N of the transformations of metric semi-symmetric N-linear connections, having the same nonlinear connection N, together with the composition of mappings are groups. We obtain some important invariants of the group msT N and we give their properties. We also study the transformation laws of the torsion and curvature d-tensor fields, with respect to the transformations of the groups TN and msT N.

Teleparallel versions of Friedmann and Lewis–Papapetrou spacetimes

This paper is devoted to investigate the teleparallel versions of the Friedmann models as well as the Lewis-Papapetrou solution. We obtain the tetrad and the torsion fields for both the spacetimes. It is shown that the axial-vector vanishes for the Friedmann models. We discuss the different possibilities of the axial-vector depending on the arbitrary functions $\omega$ and $\psi$ in the Lewis-Papapetrou metric. The vector related with spin has also been evaluated.

Projective Invariance in Cosmological Models and Dark Energy

We study theories of gravitation that are based on the Einstein – Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann – Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein – Cartan – Sciama – Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of “turning on” the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period.

Torsion and magnetic field effect in the impedance of FeSiBNbCu soft magnetic amorphous wires

The magnetoimpedance (MI) effect (influence of magnetic field), torsion impedance effect (influence of torsional stresses) and a torsion magnetoimpedance (effect produced by torsion in the magnetoimpedance effect) are shown for Fe 73.5 Si 13.5 B 9 Nb 3 Cu 1 as-cast wires. The results can be explained by the influence of torsion induced anisotropy in the magnetization processes at the chosen drive current frequency of 1 MHz. Resistance and reactance responses of 40% and 48%, respectively are found.