Gravitational Fields and Nonlinear σ-Models

It is shown that different types of gravitational fields can be analyzed as nonlinear -models. We show that the Einstein—Hilbert action for stationary aximmetric fields, Einstein—Rosen gravitational wave, and Gowdy cosmological models can be expressed in terms of a Lagrangian density for the SL(2, R)/SO(2) -model. We discuss the possibility of using these results to quantize gravitational fields.     

Some double-valued representations of the linear groups

We review the mathematical theory ofSL(n, R) and its double-covering group , especially forn = 2, 3, 4. After discussing a variety of physical applications, we show that provides holonomic curved space (world) spinors with an infinite number of components. We construct the relevant holonomic manifield and discuss the gravitational interaction of a proton as an example.Invited paper, dedicated to Eugene Paul Wigner on the occasion of his eightieth birthday.Supported in part by a U.S. Department of Energy Research Grant.     

Parametrization of the Moduli Space of Flat SL(2, R) Connections on the Torus

The moduli space of flat SL(2, R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2, R) matrices modulo simultaneous conjugation by SL(2, R) matrices. Their spectral properties allow a classification of the equivalence classes, and a unique canonical form is given for each of these. In this way the moduli space becomes explicitly parametrized, and has a simple structure, resembling that of a cell complex, allowing it to be depicted. Finally, a Hausdorff topology based on this classification and parametrization is proposed.     

Generalised Split Octonions and Their Transformation in SO(7) Symmetry

Generators of \(\operatorname{SO}(8)\) group have been described by using direct product of the Gamma matrices and the Pauli Sigma matrices. We have obtained these generators in terms of generalized split octonion also. These generators have been used to describe the rotational transformation of vectors in \(\operatorname{SO}(7)\) symmetry group.     

SL(2,C)-gauge theory andN=1 supergravity

It is shown that as Riemannian space may be taken to give rise to a Poincaré gauge theory of gravitation, the superspace where the coordinates are given by (X, ), being a spinorial variable gives rise to anSL(2, C)-gauge theory and corresponds toN= 1 supergravity. It leads to a conserved current and the conserved quantity here corresponds to isospin, where the latter is taken to be generated from conformal reflection. Thus, supergravity plays a predominant role in the microlocal space-time.     

SL(4, R)-invariant chiral fields

Using a method developed before a set of exact solutions of the chiral equations , wheregSL(4,R) are presented.Work supported in part by CONACYT, México.     

<Emphasis Type="Italic">SL(2; R)</Emphasis> Duality of the Noncommutative DBI Lagrangian

We study the action of the SL(2; R) group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some consistent relations we observe that the noncommutative (or ordinary) DBI Lagrangian and its SL(2; R) dual theory are dual of each other. Therefore, we find some SL(2; R) invariant equations. In this case the noncommutativity parameter, its T -dual and its SL(2; R) dual versions are expressed in terms of each other. Furthermore, we show that on the effective variables, T -duality and SL(2; R) duality do not commute. We also study the effects of the SL(2; R) group on the noncommutative Chern–Simons action.     

Casimir operators for infinite-dimensional representations ofosp(1,2) andosp(1, 4) lie superalgebras

All independent Casimir operatorsK _2j , 1 j n, are considered for the Schurean -dimensional representations ofosp(1, 2n),n= 1,2, that were constructed recently. For these representations (which are expressed in terms of tensor products of linear differential operators andN byN matrices belonging to a finite set and depending on a real parameter) a method is presented by which the differential-operator part of operators K_2j is effectively eliminated and expressions for K_2j via matrices in are obtained. In the same way we treat the Casimir operators _2j of the even subalgebra sp(2n, ) osp(1, 2n). The eigenvalues of K_2j and _2j are evaluated as functions of the parameter for the representations of osp(1, 2) withN= 2 and ofosp(1, 4) withN = 2, 4.     

General formulation for proton decay rate in minimal supersymmetric SO(10) GUT

We give an explicit formula for the proton decay rate in the minimal renormalizable supersymmetric (SUSY) SO(10) model. In this model, the Higgs fields consist of the 10 and SO(10) representations in the Yukawa interactions with matter and of the 10, , 126, and 210 representations in the Higgs potential. We present all the mass matrices for the Higgs fields contained in this minimal SUSY SO(10) model. Finally, we discuss the threshold effects of these Higgs fields on the gauge coupling unification.Received: 8 March 2005, Published online: 8 June 2005PACS: 12.10.-g, 12.10.Dm, 12.10.Kt     

Redshift drift constraints on f(T) gravity

We explore the impact of the Sandage−Loeb (SL) test on the precision of cosmological constraints for f(T) gravity theories. The SL test is an important supplement to current cosmological observations because it measures the redshift drift in the Lyman-α forest in the spectra of distant quasars, covering the “redshift desert” of 2≲z≲5. To avoid data inconsistency, we use the best-fit models based on current combined observational data as fiducial models to simulate 30 mock SL test data. We quantify the impact of these SL test data on parameter estimation for f(T) gravity theories. Two typical f(T) models are considered, the power-law model f(T)_PL and the exponential-form model f(T)_EXP. The results show that the SL test can effectively break the existing strong degeneracy between the present-day matter density Ω_m and the Hubble constant H₀ in other cosmological observations. For the considered f(T) models, a 30-year observation of the SL test can improve the constraint precision of Ω_m and H₀ enormously but cannot effectively improve the constraint precision of the model parameters.     

SL(2,C)-gauge theory,N=1 supergravity and torsion

It is shown that the SL(2,C)-gauge theory of gravitation may be considered to correspond toN = 1 supergravity and the conserved current gives rise to the Einstein-Cartan action. The torsion term here appears due to the spinorial variable, which is associated with the internal helicity giving rise to the isospin algebra from the conformal reflection group. In this sense, the internal symmetry of hadrons is found to take a dominant role in gravitational phenomena in the microlocal space-time region where the Einstein-Cartan action becomes significant.     

Adsorption,Desorption, Dissoziation und Rekombination von SO2 an einer Palladium(111)-Oberfläche

Adsorption, Desorption, Dissociation and Recombination of SO₂ on a Palladium (111) Surface The adsorption, desorption as well as decomposition- and recombination-reactions of SO₂ on Pd(1 1 1) were studied for temperatures T = 160-1200 K using LEED, AES, thermal desorption-mass-spectrometry and molecular beam techniques. At 160 K SO₂ adsorption with an initial sticking coefficient s₀ = 1 is molecular and non-ordered; it is characterized by a precursor state and leads to a saturation coverage Θ ≈ 0,3. Heating up the adlayer SO₂ is the only desorption product, namely directly from (SO₂)_ad in the α-peak (T_max = 240 K) and as the product of recombination of (SO)_ad and O_ad in the β-peak (T_max = 330-370 K). A great part of the oxygen originating from SO₂-dissociation is incorporated into the subsurface region, resulting in an atomic S-adlayer with Θ_S = 1/7 which exhibits a (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 7 {\rm x}\sqrt 7 $\end{document}) R ± 19,1°-superstructure. This structure is also observed, if a 320 K-SO₂-exposure induced (2 × 2)-SO saturation layer with Θ_SO = 0,5 is heated up or if SO, is exposed at T > 500 K, where it corresponds to Θ_S, values of 3/7 and 2/7, respectively. Furthermore the poisoning effect of adsorbed sulfur on the dissociative O₂,-adsorption and the oxidation of sulfur by heating up an O? S-coadsorption layer were studied. As a result the following kinetic parameters (activation energies and frequency factors) were determined: .     

Integrable spin chain for the SL(2,R)/U(1) black hole sigma model

We introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-Hermitian "Hamiltonian" and show, using mostly analytical techniques, that it is described at low energies by the SL(2,R)/U(1) Euclidian black hole conformal field theory. This identification goes beyond the appearance of a noncompact spectrum; we are also able to determine the density of states, and show that it agrees with the formulas in [J. Maldacena, H. Ooguri, and J. Son, J. Math. Phys. (N.Y.) 42, 2961 (2001)] and [A. Hanany, N. Prezas, and J. Troost, J. High Energy Phys. 04 (2002) 014], hence providing a direct "physical measurement" of the associated reflection amplitude.     

The (2+1) Dirac Equation with a Delta Potential

In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric (r–r ₀) potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of r ₀ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.     

Energy dependence of the isotopic effect in the (n,p) reaction on the germanium isotopes

Cross sections for^70,72,73,74Ge(n, p)^70,72,73,74Ga,⁷⁰Ge(n, 2n)⁶⁹Ge,⁷²Ge (n,)⁶⁹Zn ^m and⁷⁴Ge(n, )⁷¹Zn ^m reactions are measured in the energy range from 13.0 to 16.6 MeV by the activation method using Ge(Li) detector-ray spectroscopy and compared with predictions of the reaction model incorporating preequilibrium and equilibrium emission mechanisms to interpret the energy dependence of the isotopic effect occuring in the (n, p) reaction. The fitted single-particle state-density parametersg, determined here for the germaniums are discussed together with theg-values found previously for the Se, Zr and Pd isotopic chains. A validity of the consistency condition between the precompound and compound models, which relatesg to the experimental level-density parametera viaa= ² g/6 is demonstrated.     

Star products for SL(2)

The deformation program (the use of star products in harmonic analysis) leads to the definition of an adapted Fourier transform, unitary transformation between spaces of square integrable functions of the group G and on the dual of its Lie algebra, describing the unitary dual of G and its Plancherel transform. This Letter is an application of this program to the universal covering group of SL(2).     

Kinematics and dynamics off(R) theories of gravity

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalisedf(R) theories of gravity. In view of the usefulness of this alternative framework to general relativity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generalise, as an example, the results of Maartens and Taylor to show that within the framework of generalf(R) theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann-Lemaître-Robertson-Walker only if the fluid has in addition a barotropic equation of state. It then follows that the Ehlers-Geren-Sachs theorem and its almost extension also hold forf(R) theories of gravity.     

Some double-valued representations of the linear groups

We review the mathematical theory of SL(n, R) and its double-covering group \(\overline {SL}\) (n, R), especially for n=2, 3, 4. After discussing a variety of physical applications, we show that \(\overline {SL}\) (3, R) provides holonomic curved space (“world”) spinors with an infinite number of components. We construct the relevant holonomic “manifield” and discuss the gravitational interaction of a proton as an example.     

Exact solutions of the SO(3)-invariant nonlinear O-model in the special theory of relativity

Exact solutions for the four-dimensional SO(3)-invariant-model are obtained using the relation between groups of isometric motions in the space-time V₄ and chiral space U_N. A means for separating corresponding solutions in the two-dimensional-model is found. It is shown that the classical instanton and meron solutions correspond to consistent rotation of V₄ and U₂, and a general solution for this case is obtained. Four-dimensional analogs of free fields for two-dimensional-models are considered using a local approach. A non-trivial general solution which diverges logarithmically is given for the SO(N)-invariant-model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 22–26, October, 1985.In conclusion I would like to thank G. G. Ivanov for his statement of the problem and useful discussions and D. Maison from Munich for delivering study [10].     

Absence of Subsystems for the Haag–Kastler Net Generated by the Energy-Momentum Tensor in Two-Dimensional Conformal Field Theory

We show that if A is the Haag–Kastler net generated by the energy-momentum tensor in a chiral quantum field theory, then every subsystem B A which is covariant under the action of SL(2,R given on A must coincide with A. The result is valid for all the allowed values of the central charge and is obtained using scaling limit techniques.