Exponentiation of large N singularities in QCD

Large N singularities of parton densities are related by a gauge transformation to a class of collinear singularities. We prove on this basis that the effective anomalous dimension shows [α_S(Q²) log N]^p singularities which are calculable to all orders by a change of scale in α_S(Q²).     

Cosmological singularities and higher-order gravitational lagrangians

General relativity is modified by adding terms proportional to R² and R^μνR_μν to the Lagrangian. One class of solutions of the modified field equations is free of singularities but does not lead to asymptotic behaviour (for large time) of the Friedmann type. A second class, which shows the correct asymptotic behaviour, does contain the usual singularities of Friedmann universes, collapse being modulated by small oscillations only. The quantum effects considered here are thus unable to prevent the occurrence of cosmological singularities under physically reasonable conditions.     

Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics

The complete set of self-consistent parameters of nominally undoped LiNbO₃ crystals of congruent composition that describe the electro-optic, piezoelectric, elasto-optic, elastic, and dielectric response has been determined by numerically evaluating available measurements. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ε^S _ij, elastic stiffness constants at constant electric field C^E _ijkl, piezoelectric stress coefficients e_ijk, elasto-optic constants at constant electric field p^E _ijkl, and clamped electro-optic coefficients r^S _ijk. It is shown that the complete set is required for calculating the effective electro-optic coefficients and dielectric constants in photorefractive applications of LiNbO₃. Received: 4 January 2002 / Revised version: 1 February 2002 / Published online: 14 March 2002     

An off-shell superspace R2-action in six dimensions

The superspace constraints corresponding to the two inequivalent versions of the 40 + 40 off-shell Weyl multiplet in six dimensions are given. A supersymmetric R²-action (including quartic fermion terms) for one of the two Weyl multiplets is constructed. A crucial role in this construction is played by the observation that there exists a formal relationship between the Weyl and Yang-Mills multiplets. Both the supersymmetric R²-action and the supersymmetric Yang-Mills F²-action coupled to the Weyl multiplet are reformulated as superspace actions.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

The scattering of strings by a black hole

We study the elastic and inelastic scattering of strings by a Schwarzschild's black hole. Pair creation takes place (and in all the modes) as a consequence of the composite structure (oscillator modes) of the string. The S-matrix amplitudes including the pair-creation rate are found at first order in √α'/R_S (√α' = Planck's length and R_S = Schwarzschild's radius). Explicit computations are made in the weak-field expansion in powers of (R_S/b)^D−3 (b = impact parameter of the string center of mass). The deflection angle and cross sections are found. The quantum string corrections to the gravitational analogue of Rutherford's scattering are computed (these are of order α'²). The pair-creation or radiation amplitude we find here is of order α', it is non-thermal and of different origin than Hawking radiation.     

The effect of relaxation on the symmetry of N.M.R. spectra

The effect of nuclear relaxation on the symmetry properties of N.M.R. spectra is examined in terms of the properties of the relaxation matrix elements R_ijkl . It is found that the symmetry relations R_ijkl = R_jilk = R_klij = Rlkij obtain for one or more dominant relaxation mechanisms under ‘extreme narrowing’ conditions. Further, the symmetry relation R_ijkl = R_{λi, λj, λk, λl} , where λ is a spin inversion operator, is shown to obtain for (a) only one dominant relaxation mechanism or (b) two dominant relaxation mechanisms which have the same commutation properties with λ. This latter symmetry relation does not obtain for two dominant relaxation mechanisms with the same order of spatial dependence and different commutation properties with λ. The effect of nuclear relaxation can therefore yield unsymmetrical first-order spectra; the application of this analysis to the determination of the absolute sign of the spin-spin coupling constants is proposed.     

Composite stokes singularities in coherently and incoherently superimposed vector optical fields

The composite Stokes singularities formed in the coherent and incoherent superposition of two vector monochromatic coherent optical fields are studied and compared analytically and numerically. It is shown that the dynamic behavior of composite Stokes singularities depends on the superposition scheme (coherent or incoherent superposition), initial spatial distributions of the two superimposed fields, and propagation distance, and for the coherent superposition additionally depends on the relative phase of the two fields. There exist S₁₂ (C-points), S₃₁, S₂₃ composite singularities, and L-lines, in particular, V-points and C-lines at the transverse plane. Generally, both V-points and C-lines are unstable. For the coherent superposition the degree of polarization P=1, whereas for the incoherent superposition P may be less than 1 and is variable upon propagation. The results are illustrated analytically and numerically.     

Polarization singularities in Young's two-slit experiment

Young's interference experiment is regarded as a two-slit diffraction phenomenon, the polarization singularities in Young's two-slit configuration illuminated with two linearly, orthogonally polarized Gaussian vortex beams are studied. It is shown that generally, there exist L-lines (linearly polarization) and polarization singularities including C-points (circular polarization), S₂₃ and S₃₁ singularities even though the parameters of two beams are the same. The pair creation-annihilation and motion of polarization singularities take place upon propagation, or by varying a control parameter, such as the amplitude ratio of two beams or obscure ratio of slits etc. For a special case of the illumination with two linearly, orthogonally polarized Gaussian vortex-free beams, polarization singularities, in particular, C-points may occur if a parameter of two beams is not equal.     

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.     

Intensity measurements for the (2, 0) γ-band of O2, b1Σ+g−X3Σ-g

Quantitative intensity measurements have been made for the oxygen γ-band at 6280 Å. Intensities for 19 individual rotational lines of the P_P and P_Q branches and the intensity of the combined R_R and R_Q branches are reported. The band intensity, S^v′_v^″, is found to be 1.52±0.07 cm^-1km^-1atm^-1 (STP).     

Zero-lapse loci in asymptotically flat maximally foliated spacetime manifolds

We settle the question of the occurrence of zero-lapse loci for maximal foliations {S_λ},S_λ ? R³, in an asymptotically flat spacetime.     

Large magnetic entropy change and refrigerant capacity in rare-earth intermetallic RCuAl (R=Ho and Er) compounds

The magnetic properties and the magnetocaloric effects of RCuAl (R=Ho and Er) compounds have been investigated. Both HoCuAl and ErCuAl just undergo a second-order ferromagnetic–paramagnetic phase transition at T_C. Large reversible magnetic entropy changes (ΔS_M) are observed around their respective Curie temperatures due to the ferromagnetic–paramagnetic phase transition. For a field change of 0–5 T, the peak values of −ΔS_M of RCuAl (R=Ho and Er) compounds are 23.9 and 22.9 J kg⁻¹ K⁻¹ at T_C, with the values of refrigerant capacity of 393 and 321 J kg⁻¹, respectively. These properties suggest that RCuAl (R=Ho and Er) compounds could be considered as attractive magnetic refrigerants working in low temperature range.     

Nonscalar singularities in spatially homogeneous cosmologies

Singularities in vacuum spatially homogeneous cosmological models are investigated. It is shown that in general the curvature scalarR _* ^abcd R^*abcddiverge and that the only solutions which have curvature singularities at which this scalar does not diverge describe certain plane-wave space-times. It is argued that with matter present these nonscalar singularities are even less likely to occur. The exceptional case of Bianchi type VI_–1/9 is not considered.     

The 18O(p, α)15N cross section at low energies

The ¹⁸O(p, α)¹⁵N reaction cross section has been measured over the energy range 661 keV > E_c.m > 223 keV. The S-function was extrapolated to energies of astrophysical interest using the R-matrix theory. The S-factor, S₀, is estimated to be 46 MeV · b which is a factor of 3 larger than the value used in a recent tabulation of nuclear reaction rates. The effects of broad levels near the proton threshold are discussed.     

Lichtausbeute von α-Teilchen in kristallinem und dampfförmigem Anthrazen

The light output,S _v by α-particles stopped in anthracene vapour has been measured as a function of vapour pressure (10–700 mm Hg) and temperature (250°C–385°C). The comparison of the results for an idealised vapour neglecting collisions with the light output,S _c, from anthracene crystals by α-particles impinging parallel to thec′-axis yields the unexpected results: S_v(8.78 MeV)/S_c(8.78 MeV)=0.46±0.05 andS _v(6.05 MeV)/S _c(6.05 MeV)=0.57±0.08. A simple model assuming quenching by collisions of the vapour molecules could explain the observed dependence of the light output on the vapour pressure at fixed temperature. The path lengthsR _v of α-particles in anthracene vapour were determined to be R_v(8.78 MeV)=(9.0±0.6) mg/cm²,R _v(6.05 MeV)=(4.9±0.6) mg/cm² and the ratio of the light output by the two different α-energiesS _v(8.78 MeV)/S _v(6.05 MeV)=1.42±0.2.     

Limits on low scale gravity from e+e−→W+W−, ZZ and γγ

It has been proposed recently that the scale of quantum gravity (“the string scale”) can be M_S∼few TeV with n≥2 extra dimensions of size R≲mm so that, at distances greater than R, Newtonian gravity with M_Pl∼10¹⁸ GeV is reproduced if M_Pl²∼RⁿM_Sⁿ⁺². Exchange of virtual gravitons in this theory generates higher-dimensional operators involving SM fields, suppressed by powers of M_S. We discuss constraints on this scenario from the contribution of these operators to the processes e⁺e⁻→W⁺W⁻, ZZ, γγ. We find that LEP2 can place a limit M_S≈1 TeV from e⁺e⁻→W⁺W⁻, ZZ, γγ.     

Snyder’s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ? _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ? _P /R ～ 10^?61.     

Measurements of intensities and nitrogen-broadened linewidths in the CO fundamental at low temperatures

Intensities and nitrogen-broadened half-widths of lines R(0), R(8) and R(16) in the fundamental band of ¹²C¹⁶O have been measured at 83°K, 100°K, 150°K, 200°K and 298°K. The intensities of several other lines in the P- and R-branches of the band have also been measured at 298°K. The absolute intensity derived from the line intensity data using the Herman-Wallis formula is S^°_v = 273 ± 10 cm^-2atm^-1 at S.T.P. A separate measurement employing the Wilson-Wells-Penner-Weber method has yielded S^°_v = 277 ± 4 cm^-2 atm^-1 at S.T.P. Both of these values are within 6 per cent of most of the previously published direct measurements of this parameter. The values for the line intensities reported earlier by other authors are lower by nearly 16 per cent.