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. PACS: 04.02 Cv, 95.30 Sf, 98.80-k     

Gravitational geometric phase in the presence of torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamics of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy–Wouthuysen approximation, the non-relativistic quantum dynamics is studied and the influence of the torsion on the Aharonov–Casher and He–McKellar–Wilkens effects are discussed. An erratum to this article can be found at     

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

We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the quantum-mechanical expectation value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases. We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev.     

A Remark on Schwarz's Topological Field Theory

The standard evaluation of the partition function Z of Schwarz's topological field theory results in the Ray–Singer analytic torsion. Here we present an alternative evaluation which results in Z=1. Mathematically, this amounts to a novel perspective on analytic torsion: it can be formally written as a ratio of volumes of spaces of differential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained.     

Schemes for excitation of rare earth monoxides in flame laser-induced molecular ionization spectrometry

Laser-induced ionization spectra of PrO, TbO, and CeO molecules in a flame were recorded in the wavelength ranges 440–480 nm and 535–575 nm. Based on study of the spectra, we propose a two-step scheme for excitation of PrO and CeO molecules in which in the first step, the molecule goes to the excited electronic state, while the excitation energy in the second step is selected so that the total energy imparted to the molecule corresponds to its ionization potential. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 544–546, July–August, 2006.     

On unified field theories,dynamical torsion and geometrical models: II

We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl., Lett. 2010. V. 7, No. 5, P. 299–307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean R ⊗ O ₃ ∼ R ⊗ SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation between the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang-Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and (iii) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only to cosmological space-time solution in eternal expansion.     

Berry phase for spin-1/2 particles moving in a space-time with torsion

Berry phase for a spin-1/2 particle moving in a flat space-time with torsion is investigated in the context of the Einstein–Cartan–Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks. Received: 12 February 2001 / Revised version: 2 May 2001 / Published online: 29 June 2001     

Teleparallel versions of Friedmann and Lewis–Papapetrou spacetimes

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

Microwave excited CO<Subscript>2</Subscript> laser with multiple units using orthogonal electric fields

The third order nonlinear optical properties of 4^′-methoxy chalcone and its derivatives have been investigated using a single-beam Z-scan technique with nanosecond laser pulses at 532 nm. The 4^′-methoxy chalcone and its derivatives are donor–acceptor–acceptor (D–A–A) and donor–acceptor–donor (D–A–D) type intramolecular charge transfer molecules. The nonlinear response in these molecules was found to increase with increase in (a) the electron acceptor strength in D–A–A type and (b) the donor strength of the substituted group in D–A–D type molecules. The χ⁽³⁾ value in these molecules is found to be of the order of 10^-13 esu. The observed increase in the third order nonlinearity in these molecules clearly indicates the electronic origin. The compounds exhibit good optical limiting at 532 nm. The best optical limiting behavior was observed with the molecule substituted by a strong electron donor. PACS 42.65.An; 42.70.Nq     

A comment on Bonnor–Steadman closed timelike curves

The existence and stability closed timelike curves in a Bonnor–Ward spacetime without torsion line singularities is shown by exhibiting particular examples.     

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.     

Unified Field Theoretical Models from Generalized Affine Geometries II

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288–1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗O ₃∼R⊗SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.     

Spin-Rotation Coupling in Gravitation with Torsion

Based on the theory of gravitation with torsion developed by Hammond [Rep. Prog. Phys. 65 (2002) 599], the interaction between the intrinsic spin of a particle and the mass source is calculated. It is shown that spin can interact with the gravitimagnetic field created by a rotational mass, where the spin-rotation coupling is also discussed. According to the recent torsion pendulum experiment with polarized electrons by Heckel et al. [Phys. Rev. Lett. 97 (2006) 021603], we set a new limit on the value of the torsion coupling constant K as K∈[0.53,0.95], which has improved many orders than the constraints from the early spin-spin experiment with K<2×10¹⁴.     

Effect of Torsion in Dirac Equation for Coulomb Potential in Robertson–Walker Space–Time

The Dirac equation with Coulomb-like potential and self-interaction term, that originates from torsion, is studied in the Robertson–Walker space–time. It is shown that the angular dependence of the equation can be separated also in presence of nonlinear terms. Under reasonable physical assumptions, the time dependence is also separated. An extended perturbative calculation can then be applied qualitatively. The conclusion is that the perturbation of the energy levels of the system, as consequence of the self-interacting term, is not relevant on physical grounds.     

Nonminimally coupled scalar field and perfect fluid in Einstein–Cartan cosmology

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field and perfect fluid. Some effects of torsion are revealed by solving an analogous problem in general relativity. A comparative analysis of the cosmological models with and without perfect fluid is carried out in context of the Einstein–Cartan theory. The role of perfect fluid in the dynamics of models is discussed.     

Energy and Momentum Densities of Cosmological Models,with Equation of State <Emphasis Type="Italic">ρ</Emphasis>=<Emphasis Type="Italic">μ</Emphasis>, in General Relativity and Teleparallel Gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann–Thomson and Landau–Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex’s value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.     

Spherically symmetric solution in a space–time with torsion

By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein–Cartan equations of motion, corresponding to a space–time threaded with a three-form Kalb–Ramond field strength. The solution describes in its more generic form, a space–time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution and to a exact solution with a localized scalar field and a torsion kink, already reported in literature. In the process we have found evidence towards the construction of more new solutions.     

扭摆系统中扭杆的等效转动惯量——圆柱杆扭转振动的研究

研究扭摆系统中扭杆的质量或转动惯量对扭摆运动的影响,引入一个概念:扭摆系统中扭杆的等效转动惯量.纠正了一些文献在相关问题上的误解.     

Geometry of Hyper-Kähler Connections with Torsion

The internal space of a N = 4 supersymmetric model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy in SP(n). We study the mathematical background of this type of connection. In particular, we relate it to classical Hermitian geometry, construct homogeneous as well as inhomogeneous examples, characterize it in terms of holomorphic data, develop its potential theory and reduction theory. Received: 1 October 1999 / Accepted: 30 January 2000     

Geometric classification of the torsion tensor of space‐time

Torsion appears in literature in quite different forms. Generally, spin is considered to be the source of torsion, but there are several other possibilities in which torsion emerges in different contexts. In some cases a phenomenological counterpart is absent, in some other cases torsion arises from sources without spin as a gradient of a scalar field. Accordingly, we propose two classification schemes. The firstone is based on the possibility to construct torsion tensors from the product of a covariant bivector and a vector and their respective space‐time properties. The secondone is obtained by starting from the decomposition of torsion into three irreducible pieces. Their space‐time properties again lead to a complete classification. The classifications found are given in a U ₄, a four dimensional space‐time where the torsion tensors have some peculiar properties. The irreducible decomposition is useful since most of the phenomenological work done for torsion concerns four dimensional cosmological models. In the second part of the paper two applications of these classification schemes are given. The modifications of energy‐momentum tensors are considered that arise due to different sources of torsion. Furthermore, we analyze the contributions of torsion to shear, vorticity, expansion and acceleration. Finally the generalized Raychaudhuri equation is discussed.