Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Chiral symmetry and the A1 contribution to the nucleon-nucleon interaction

The contribution of A₁ exchange to the nucleon-nucleon potential is studied in a broken chiral symmetric model. The A₁ is treated as a finite-width resonance in the πρ s-wave. Connections between pseudoscalar and pseudovector pion-nucleon coupling in the underlying model lagrangian are studied in detail. It is found that large terms in the NN interaction arising from πρ exchange with pseudoscalar coupling are suppressed by interference with a₁ exchange. With pseudovector coupling there is a suppression of the A₁ exchange by the so-called “seagull” terms in πρ exchange which arise from gauge invariance. The suppression becomes an exact cancellation in the limit of infinite ρ and a₁ masses and exact chiral symmetry. We found that inclusion of the a₁ decay into the πρ state strongly modifies the a₁] exchange potential, suppressing the tensor part but leaving the spin-spin part almost unchanged.     

A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics.     

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension D_T=2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner-Nordström type metric is obtained.     

Pseudo-Kähler metrics on six-dimensional nilpotent Lie algebras

It is well known that any symplectic manifold (M,Ω) has an almost complex structure J which is compatible with Ω. In this paper, we deal with the existence of compatible pairs (J,Ω) on nilpotent Lie algebras of dimension ≤6, J being an integrable almost complex structure. We prove that if such a pair exists, J must satisfy some extra conditions, namely J must be nilpotent in the sense of [Trans. Am. Math. Soc. 352 (2000) 5405]. Associated to any such a compatible pair, there is a pseudo-Kähler metric g which cannot be positive definite unless be abelian. All these metrics are Ricci flat, although many of them are nonflat, and we study the behaviour of its curvature tensor under deformation.     

Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dμ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A^α μ （x） have spherical symmetry, depending only on the radial coordinate τ is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Topology change and θ-vacua in 2D Yang-Mills theory

We discuss the existence of θ-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of π₁(G) if M is orientable, and with the IUR's of π₁(G)/2π₁(G) if M is non-orientable.     

Topological Invariant in Riemann–Cartan Manifold and Space-Time Defects

In a Riemann–Cartan manifold a topologicalinvariant is constructed in terms of the torsion tensor.Using the -mapping method and the completedecomposition of the gauge potential, the topologicalinvariant is extricated from a strong restrictivecondition and is quantized in units of an elementarylength. This topological invariant is linked to thefirst Chern class and its inner structure is labeled bya set of winding numbers. In the early universe,by extending to a gauge parallel basis in internal spaceand four analogous topological invariants, thespace-time defects are formulated in an invariant form and are quantized naturally in units of thePlanck length.     

Magnetic and microstructural investigations of melt-spun Fe(NdPr)B

The magnetic behavior of rapidly solidified FePrB was investigated in the composition range Fe_77+χPr₁₅B_8−χ (0 ≤ χ ≤ 4). Furthermore, the magnetic and microstructural properties of Fe(NdPr)B were analyzed in the range Fe₇₈(Nd_χPr_1−χ)₁₅B₇ (0 ≤ χ ≤ 1). The temperature dependence of the critical field was analyzed with a modified form of Brown's expression for the nucleation field. From this analysis the values for the microstructural parameters, _K and N_eff, were determined which describe the deteriorating effects of the non-ideal microstructure on the coercivity.     

Topological charge of (lattice) gauge fields

Using recently derived explicit formulae for the 2- and 3-cochains in SU(2) gauge theory, we are able to integrate the Chern-Simons density analytically. We arrive — in SU(2) — at a local algebraic expression for the topological charge, which is the sum of local winding numbers associated with the corners (lattice points) of the cells covering the manifold plus contributions from possible isolated gauge singularities which manifest themselves as “vortices” in the 1-, 2- or 3-cochains. Among others we consider hypercubic geometry — i.e. covering the manifold by hypercubes — which is of particular interest to lattice Monte Carlo applications. Finally, we extend our results to SU(3) gauge theory.     

Nax/2Bi1−x/2MoxV1−xO4 and Bi1−x/3MoxV1−xO4 New Scheelite-related phases

New Scheelite-related solid solutions of the compositions Na_x/2Bi_1−x/2Mo_xV_1−xO₄ (0≤x≤1) and Bi_1−x/3 Mo_xV_1−xO₄(0≤x≤0.2) have been synthesised by the substitution of Na and Mo at the A and B sites respectively of the ABO₄ type ferroelastic BiVO₄. The phases were characterised using chemical analysis, powder X-ray diffraction, scanning electron microscopy, EDAX, and Raman spectroscopy. While almost a continuous solid solution is obtained for the series Na_x/2Bi_1−x/2Mo_xV_1−xO₄, the absence of Na at the A-site results only in a narrow stability region for the other series, Bi_1−x/3 Mo_xV_1−xO₄ where 0≤x≤0.2. Raman spectra of selected samples at room temperature also suggest that vanadium and molybdenum atoms are disordered at the tetrahedral sites.     

Duals for Non-Abelian Lattice Gauge Theories by Categorical Methods

We introduce duals for non-Abelian lattice gauge theories in dimension at least three by using a categorical approach to the notion of duality in lattice theories. We first discuss the general concepts for the case of a dual-triangular lattice (i.e., the dual lattice is triangular) and find that the commutative tetrahedron condition of category theory can directly be used to define a gauge-invariant action for the dual theory. We then consider the cubic lattice (where the dual is cubic again). The case of the gauge group SU(2) is discussed in detail. We will find that in this case gauge connections of the dual theory correspond to SU(2) spin networks, suggesting that the dual is a discrete version of a quantum field theory of quantum simplicial complexes (i.e. the dual theory lives already on a quantized level in its classical form). We conclude by showing that our notion of duality leads to a hierarchy of extended lattice gauge theories closely resembling the one of extended topological quantum field theories. The appearance of this hierarchy can be understood by the quantum von Neumann hierarchy introduced by one of the authors in previous work.     

The anomalous behaviour of Gd atoms (Fe1−xMnx)2 compounds

The educed Gd atoms in the X-structure (Th₆Mn₂₃-type) of Gd(Fe_1−xMn_x)₂ were magnetically investigated by comparing with Gd₆(Fe_1−yMn_y)₂₃ whose structure is Th₆Mn₂₃-type. The magnetic properties of Gd(Fe_1−xMn_x)₂ (0.4≤x≤0.7) were observed to be quite similar to those of Gd₆(Fe_1−yMn_y)₂₃ (0.4≤y≤0.7).     

Riemannian curvature on the group of area-preserving diffeomorphisms (motions of fluid) of 2-sphere

Euler's equation for an incompressible fluid filled in a Riemannian manifold D is regarded as a geodesic equation on the group of volume-preserving diffeomorphisms of D provided with a one-sided invariant metric. A negative sectional curvature implies instability of the geodesic with respect to the corresponding flow and perturbation. The exponential growth of the perturbation is estimated from the values of the sectional curvatures.

This paper presents the expression of the components of Riemannian curvature tensor of the group of area-preserving diffeomorphisms of a 2-sphere in explicit formulas through 3 − j coefficients.     

Phase segregation of LixMn2O4 (0.6<x<1) in non-equilibrium reduction processes

Chemical synthesis routes to Li_xMn₂O₄ (0.15≤x≤1) in non-equilibrium reduction processes were developed to carry out detailed structural analysis. Non-equilibrium Li_xMn₂O₄ (0.15≤x≤1) samples were prepared by chemical lithiation of λ-MnO₂ with LiI for 24 h; longer than 1 week was needed to reach true equilibrium at room temperature. The samples were characterized by X-ray diffraction analysis. The phase diagram was different from that in the equilibrium state; three cubic phases (phases A, B and C) were observed for Li_xMn₂O₄ (0.15≤x≤1). There were two regions of two-phase coexistence: the region of 0.25<x<0.55 (phase B+phase C) and 0.6<x<1.0 (phase A+phase B). In the compositional range of 0.6<x<1.0, the lattice constants of phases A and B change with the lithium composition, this indicates that it is a structural anomaly with a metastable two-phase character in non-equilibrium reduction processes.     

The Duality Transformation for an n-Species Ising Model Interacting with Z2 Gauge Fields on a Random Surface

The duality transformation is carried out for an n-species Ising spin system interacting with Z₂ gauge fields. For n > 1, we find that the dual model has topological terms when the surface is topologically nontrivial. The plaquette interaction of the gauge fields is dual to an n-spin coupling in the dual model.     

The structure of the Newtonian limit

We consider a smooth one-parameter family of four-dimensional manifolds X,≥0, each one endowed with a covariant metric g. It is assumed that g is a Lorentz metric for each >0, i.e., the signature of g is (+,−,−,−) for >0, while the limit metric g₀ on X₀ is assumed to be degenerated of rank 1, i.e., the signature of g₀ is (+,0,0,0). We characterize when the limit manifold X₀ inherits the geometric structure of a Newtonian gravitation. The limit manifold X₀ is a Newtonian gravitation if and only if there exist the limits of the Levi-Civita connection , the curvature operator and the contravariant Einstein tensor G² as →0. Moreover, the existence of these limits is characterized in terms of the Taylor expansion of the family {g} with respect to the parameter .