Spin-torsion Coupling Research Articles

Hyperfine interactions and internal rotation in methanol.

We present a rigorous derivation of the nuclear spin-rotation and spin-torsion coupling terms in the hyperfine Hamiltonian for molecules with internal rotation. Our formulas differ from the expressions derived by Heuvel and Dymanus [J. Mol. Spectrosc. 47, 363 (1973)], which these authors used and which were also applied recently by others to interpret experimental hyperfine spectra of such molecules. In the present work, our theoretical results are applied to methanol. We calculate the nuclear spin-spin magnetic dipole-dipole interactions and the nuclear contribution to the spin-torsion coupling vectors from the nuclear coordinates as functions of the internal rotation angle γ, compute the spin-rotation coupling tensors by ab initio electronic structure methods also as functions of γ, and obtain the missing parameters for the electronic contribution to the spin-torsion coupling from a fit to measured spectra. The resulting hyperfine Hamiltonian is then used to compute hyperfine transition frequencies and intensities for twelve torsion-rotation transitions in methanol. With the use of the ab initio calculated spin-rotation coupling parameters without any modification, and physically reasonable values for the spin-torsion coupling parameters from the fit, we find good agreement with all of the measured spectra.

Spin-torsion effects in the hyperfine structure of methanol.

The magnetic hyperfine structure of the non-rigid methanol molecule is investigated experimentally and theoretically. 12 hyperfine patterns are recorded using molecular beam microwave spectrometers. These patterns, along with previously recorded ones, are analyzed in an attempt to evidence the effects of the magnetic spin-torsion coupling due to the large amplitude internal rotation of the methyl group [J. E. M. Heuvel and A. Dymanus, J. Mol. Spectrosc. 47, 363 (1973)]. The theoretical approach setup to analyze the observed data accounts for this spin-torsion in addition to the familiar magnetic spin-rotation and spin-spin interactions. The theoretical approach relies on symmetry considerations to build a hyperfine coupling Hamiltonian and spin-rotation-torsion wavefunctions compatible with the Pauli exclusion principle. Although all experimental hyperfine patterns are not fully resolved, the line position analysis yields values for several parameters including one describing the spin-torsion coupling.

Spin-torsion coupling and gravitational moments of Dirac fermions: Theory and experimental bounds

We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltonian for the Dirac particle coupled to magnetic field in a noninertial reference system, we analyze the recent experimental data and obtain bounds on the spacetime torsion.

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density $\epsilon\propto gT^4$ was on the order of $n^2/m_\textrm{Pl}^2$ (in natural units), where $n\propto gT^3$ is the fermion number density and $g$ is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles ($g\approx 100$), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about $10^{32}$ times smaller than its present value, giving $\approx 50 \mum$. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.

Four-fermion interaction from torsion as dark energy

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein–Cartan–Sciama–Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.

THE SPIN-TORSION COUPLING AND CAUSALITY FOR THE STANDARD MODEL

We study the influence of the spin-torsion coupling prescription and we prove the causal propagation for the fields of the standard model.

Gravitomagnetic Effect and Spin-Torsion Coupling

We study the gravitomagnetic effect in the context of absolute parallelism with the use of a modified geodesic equation via a free parameter b. We calculate the time difference in two atomic clocks orbiting the Earth in opposite directions and find a small correction due to the coupling between the torsion of the spacetime and the internal structure of atomic clocks measured by the free parameter.

SPIN-ROTATION COUPLING EFFECTS ON THE STRUCTURE FORMATION IN GÖDEL UNIVERSE AND COBE DATA

A rotating universe represented by the Gödel metric in spacetimes with Cartan torsion is investigated. The spin–torsion coupling is shown to contribute to the structure formation in an apppreciable way only at the early stages of the universe. To demonstrate these conjectures, we have made use of a spinning fluid model in Einstein–Cartan gravity. We also show that autoparallel equation in Riemann–Cartan spacetime leads to the evolution equation of the cosmological perturbation where the spin-rotation coupling contributes to the growth of inhomogeneities through a constant term. From this idea, one is able to estimate that torsion in the Planck era is around 1015 s -1 where COBE constraint on temperature fluctuations is used in this computation. A spin density of the universe of 1053 g · cm -1 s -1 is also obtained in our framework.

Torsion and electron motion in quantum dots with crystal lattice dislocations

The motion of a conducting electron in a quantum dot, with one or several dislocations in the underlying crystal lattice, is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of torsion are investigated on the levels of classical motion, on non-relativistic quantum motion, and on spin-torsion coupling terms derivable in the non-relativistic limit of generalizations of the Dirac equation in a space with torsion. Finally, phenomenological spin-torsion couplings analogous to Pauli terms are considered in the non-relativistic equations. Different prescriptions of classical and non-relativistic quantum motion in a space with torsion are shown to give effects that should, in principle, be observable. Semiclassical arguments are presented to show that torsion is not relevant for the classical motion of the centre of a wavepacket. The correct semiclassical limit can instead be described as classical trajectories in a Hamiltonian given by the band energy. In the special case of a spherically symmetric band this motion reduces to straight lines, independently of local crystal orientations. By dimensional analysis the coupling constants of the possible spin-torsion interactions are postulated to be proportional to a combination of the effective mass of the electron, , the lattice constant, a, and . The level splitting is then very small with transition frequencies of the order of 1 kHz, or smaller.

The neutrino magnetic moment in the early universe

We consider a spin-torsion coupling for neutrinos in the early universe and show that a neutrino magnetic moment can be present also for zeromass neutrinos. We make an estimate of this induced magnetic moment just prior to the nucleosynthesis and it happens that it is of the same magnitude as that obtained in the Weinberg-Salam electroweak theory; moreover it is temperature dependent.

Generalised affine geometry and algebraically extended relativity-a new approach to spin-torsion coupling

A geometric theory of gravitation with spin-torsion coupling is proposed. The theory could be interpreted either as general relativity based on a generalised affine connection, or alternatively as an algebraically extended general relativity over the algebra of hypercomplex numbers. According to the algebraically extended interpretation the torsion tensor must be totally antisymmetric. In this case the authors also have a geometric symmetry corresponding to spin-reversal invariance. The simplest Lagrangian density within this theory is that of the Einstein-Cartan theory, but where torsion is determined by an antisymmetric torsion potential. The conservation laws of the theory correspond to conservation of energy-momentum and spin-angular momentum.

Motion of photons in scalar-tensor theory of gravitation with spin-torsion coupling

From a geometric interpretation of the Brans-Dicke theory it is argued that the Brans-Dicke scalar field may also play the role of a torsion potential. Minimal coupling of electromagnetism to gravitation then leads to a modified gauge invariance and modified equations of motion of the photon. In the present paper the effect of this photon-torsion coupling is studied. In particular the question whether this photon-torsion-scalar coupling could relax the restrictive experimental bounds on the Brans-Dicke coupling is investigated. This calculation is done within the semiclassical quantised theory. It is found that the photon-torsion interaction has a negligible effect on the motion of photons in the gravitational field of the Sun.

Magnetic fields in the early universe

We consider some mechanisms which can be responsible for the formation of a magnetic field in the early universe. It happens that introducing the spin-torsion coupling interaction a magnetic field results, compatible with observation data, which may be important in the process of galaxy formation.

The Spin-Torsion Coupling Precession of Spin and its Effects on Single Pulses of Pulsars

The Spin-Torsion Coupling Precession of Spin and its Effects on Single Pulses of Pulsars

Dirac general covariance and tetrads. I. Clifford and Lie bundles and torsion

The isomorphic map of Clifford and Lie bundles to arbitrary coordinate atlases using a global orthonormal tetrad field on a parallelizable space-time is used to construct a fully covariant Dirac spinor theory. The Klein–Gordon equation exhibits a natural spin-torsion coupling of the Einstein–Cartan form, the torsion coming from the tetrad field. The tetrad connection coefficients are explicitly derived in addition to their relationship to the usual Levi–Cività coefficients. Various topological conditions for vanishing torsion are given. The Dirac and adjoint Dirac equations are obtained from a simple Lagrangian and the structure of the adjoint equation is discussed.

On the Maxwell equations in a Riemann-Cartan space

Considering the vacuum polarization effect in the presence of torsion, the modifications of the Maxwell equations are explicitly computated to first order in the spin-torsion coupling constant.

On a possible unification of gravitational and weak interactions

Within the framework of Cartan's generalization of Einstein's theory of gravitation one can achieve a unification of gravitational and weak interactions by appropriate choice of the parameter that couples spin and torsion. The proposed spin-torsion coupling has negligible cosmic effects except at stages of evolution when 1081 nucleons are confined to a sphere with a radius of about one astronomical unit. For a single nuclear particle the gravitational effects of mass and spin balance at a radius of about 1% of its Compton wavelength, thus stabilizing it against gravitational collapse.