Cosmological solutions with Calabi-Yau compactification

Assuming a Calabi-Yau compactification, cosmological solutions are presented in ten-dimensional, N=1 Yang-Mills supergravity theory with the curvature squared term (R²_μνϱσ −4R_μν² + R²). In a vacuum state, Kasner-type soluti ons exist as well as (four-dimensional Minkoswki space-time)×(a Calabi-Yau space). In the later stage of the universe the (four-dimensional Friedmann universe)×(a constant Calabi-Yau space) is realized asymptotically like an attractor. This solution is asymptotically stable against small perturbations.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

In-out semi-classical gravity and 1N quantum gravity

Classical gravity with higher derivatives, when coupled to the in-out matrix element of T_μν: (a) appears to be free from instabilities of the in-in theory; (b) may be considered as the “underlying classical theory” to Tomboulis' $\text{1}\text{N}\text{-}\text{resummed}$ quantum gravity. I explain how these two facts may be adduced as evidence for the viability both of the former semi-classical approximation and of the latter approach to full quantum gravity.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling $\text{g}\text{(t), t =}\text{ln}\text{[}\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{)}{}^2\text{μ}{}^4\text{]}$. The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F_μν^a = 0, and ferromagnetism, for which (F_μν^a)² = λ², i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.     

The axial anomaly and anti-symmetric tensor fields

Spin-$\text{1}\text{2}$ fermions are coupled to external axial vector and rank-2 anti-symmetic tensor fields. The chiral U(1) Ward identity is shown to have anomalous structure given by $\text{F}{}_{\mathrm{\mu \nu }}\text{F}\text{?}{}^{\mathrm{\mu \nu }}$ only with F_μν the axial vector field strength tensor. No Additional axial anomalied are introduced due to the presence of the anti-symmetric tensor fields.     

The axial anomaly for spin 32 fields

The axial anomaly for a Majorana spin $\text{3}\text{2}$ loop with external gravitons in supergravity is ?_μJ^μ₅ = (192π²)^??^αβ?σR?σ^μνRμναβ. This is twice the value of the corresponding anomaly for a Dirac spin $\text{1}\text{2}$ loop.     

In search of scalar gluonium

We discuss a scalar meson coupled strongly to gluons. Radiative decays of the J/ψ are taken as a source of gluons so that our aim is to calculate Γ(J/ψ→σγ), where σ is the presumed scalar gluonium. We use QCD sum rules to find both 〈0|α_sG_μν^aG_μν^a|σ〉 (where G_μν^a is the gluon field strength tensor) and Γ(J/ψ→σγ) in terms of 〈0|α_sG_μν^aG_μν^a|σ〉. The final prediction for the width is expected to be valid within a factor of two and gives $\text{Γ(}\text{J}\text{/ψ→σγ→}\text{two pions in S-wave}\text{+ γ) ? 25}\text{eV for}\text{m}{}_{\mathrm{\sigma }}\text{= 700}\text{MeV}$. Non-perturbative QCD naturally explains the observed asymmetry between scalar and pseudoscalar states in the radiative decays of the J/ψ. Some general remarks on gluonium in QCD are made.     

Dynamical basis for spin-12 as well as generation stability of leptons and quarks

A three-way preon interaction with a spin-dependence of the form σ_μν⁽¹⁾ σ_νγ⁽²⁾ σ_λμ⁽³⁾, is proposed for a two-flavor (t,v) preon model, within a Bethe-Salpeter framework. This mechanism not only eliminates all $\text{S =}\text{3}\text{2}$ states but severely restricts the spatial symmetries of allowed $\text{S =}\text{1}\text{2}$ states to at most threedistinct “generations” with very strong selection rules forbidding transitions among them.     

Effects of Eu3+  Fe3+ exchange interaction on the spin Hamiltonian parameters of Fe3+ in EuGaG

The anisotropic exchange $\text{1}\text{3}\text{a}{}_{\mathrm{\mu \nu }}\text{Y}{}_{\mathrm{\mu \nu }}\text{(L}{}_{\mathrm{<mtext>Eu</mtext>}}\text{)S}{}_{\mathrm{<mtext>Eu</mtext>}}\text{· S}{}_{\mathrm{<mtext>Fe</mtext>}}\text{(0 < μ ? 6)}$ is incorporated with the isotropic exchange ?2 a₀₀S_Eu · S_Fe to interpret the observed spin-Hamiltonian parameters g and D of Fe³⁺ doped into EuGaG. Calculations from the observed g shifts yield a value of a₀₀ equal to 0.01 K. In order to explain the observed D shift, it is concluded that the spherical harmonics Y_μν(L_Eu) with μ > 2 are of dominant importance.     

Critical behaviour of the electrical resistance of holmium near the Néel temperature

A detailed study of the electrical resistance, R(T), of a c-axis single crystal of holmium has been made in the vicinity of its Néel point. The results suggest that the critical temperature dependence of $\text{d}\text{R}\text{d}\text{T}$ is determined by short range correlations for both T → T^-_N and T → T⁺_N, although long range correlations become important in the paramagnetic state.     

Franck-condon factors for diatomic molecules and the factorization method

By means of the factorization method, recurrence relations for the matrix elementS$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦r}{}^{\mathrm{N}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ for an arbitrary positive integer N are obtained in the framework of α-averaging for the Morse potential. The method of calculating the matrix element$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦R}{}_{\mathrm{<mtext>e</mtext>}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ is outlined, provided a dependence of the electronic transition moment R_e on the internuclear distance r can be approximated by the polynomial R_e(r)=a₀+a₁r+a₂r²+…+ainNr^N. Recurrence relations are also obtained for the case of the exponential dependence R_e(r).     

The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras

We construct the general coupling of nN = 2 Maxwell super-multiplets to N = 2 supergravity in five spacetime dimensions. In the case that the scalar field manifold is symmetric we find a complete classification based on Jordan algebras. Apart from the generic case there are also four “exceptional” cases associated with the Jordan algebras J₃^$\text{A}$ of 3 × 3 hermitian matrices over the division algebras $\text{A}\text{=}\text{R}\text{,}\text{C}\text{,}\text{H}\text{,}\text{O}$. Similar results follow for four dimensions, by dimensional reduction.     

Tunable diode laser measurements of the band strength and collision halfwidths of nitric oxide

The strength of the fundamental absorption band of nitric oxide at 5.3 μm and collision halfwidths of nitric oxide lines broadened by nitrogen, argon, and combustion gases were measured in absorption cell, flat flame and shock tube experiments using a tunable diode laser. Room temperature absorption measurements were made in an absorption cell filled with NO/N₂ or NO/Ar mixtures or with probe-extracted combustion gases. High temperature (to 2500 K) absorption measurements were performed for NO in N₂ and NO in Ar using a shock tube, and for NO in combustion gases using a flat flame burner.Absorption measurements were made on lines from 1860–1925 cm^?1, ($\text{Ω=}\text{1}\text{2}$ and $\text{3}\text{2}$,P($\text{5}\text{2}$-R ($\text{29}\text{2}$)) resulting in a band strength of 123±8 cm^-2 atm^?1 at 273.2 K. Collision halfwidth dependencies for each broadening species were examined as a function of rotational quantum number and temperature.     

Gravitational Field Equations of Fourth Order and Supersymmetry

We discuss the field equations which stem from a variational principle containing the quadratic terms αR_μνR_μν and βR² besides the Einstein-Hilbert Lagrangian R. Comparison of this theory with a pure theory of fourth order shows that R must necessarily be included if we wish to interpret the field equations as gravitational equations. The Einstein-Bach-Weyl theory (α = ?3β) has the property of being a theory of “supergravitation”. Apart from gravitons without rest-mass, we have here only one additional kind of particles with rest-mass. Their mass may be determined by Planck' slength (hG/c³)^1/2. The occurrence of those particles results from the breakdown of a “supersymmetry”, that is of the conform invariance. The Einstein tensor E_μν ? R_μν ?1/2g_μνR can be regarded as a source of the gravitons without rest-mass.     

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant G_f ? 10³⁸G_N (G_N being the Newtonian constant) and a cosmological term λ_f ?;_μν (?;_μν is strong gravity metric and λ_f ～ 10²⁸ cm^? is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature ～10^?14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length ～2 × 10^?14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-$\text{1}\text{2}$ particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.     

Observation of muon pairs in neutrino interactions at Serpukhov 70 GeV accelarator

A search for dimuons produced in a spark chamber experiment in neutrino and antineutrino beams of the Serpukhov accelerator is reported. The clear dimuon signal has been observed in vN interactions. R_v = N(2ω)/N(1ω)? (6.2 ± 1.7) × 10^?3 in the energy interval 7.5 ÷ 30 GeV. From antineutrino data we conclude that in the same energy range $\text{R}{}_{\mathrm{<mtext>v</mtext>}}\text{? 1.1. × 10}{}^{\mathrm{?2}}\text{(90\% C.L.)}$.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

Frustrated magnetic structures: II. Antiferromagnetic structure of the ordered modified pyrochlore NH4FeIIFeIIIF6 at 4.2 K

The nuclear and magnetic structures of the ordered modified pyrochlore NH₄Fe²⁺Fe³⁺F₆ were solved at 4.2 K. NH⁺₄ tetrahedra are almost regular ($\text{〈}\text{N}\text{?}\text{H}\text{〉 =}\text{0.924}\text{A}\text{?}$) and the fluorinated skeleton at 4.2 K does not exhibit large deviations from the room-temperature positions (R_N = 0.042). Below T_N = 19 ± 1 K the magnetic and nuclear cells are identical. The strictly antiferromagnetic arrangement of Fe²⁺ spins (μ = 3.12(9)μB) along the [0 1 0] direction contrasts with the canted antiferromagnetic sublattice of Fe³⁺ ions (μ = 4.13 [8] μB) which is quasi-orthogonal (α = 76°) to the Fe²⁺ sublattice (R_mag = 0.078). The main component of Fe³⁺ moments lies along a. The antiferromagnetism of NH₄Fe³⁺Fe³⁺F₆ is compared to the spin-glass like behaviour which occurs when M²⁺ and M³⁺ ions are randomly distributed on the cationic sites.