Gauge theory of fermions onR × S 3 spacetime

A Lorentz-invariant gauge theory for massive fermions on R × S ³ spacetime is built up. Using the symmetry of S ³,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S ³ spacetime, pointing out major differences from the Minkowskian case.     

Loop corrections to the E8 × E8 heterotic string effective lagrangian

One-loop corrections to the effective lagrangian for the E₈ × E₈ heterotic string theory are worked out. The resulting terms are of order α′³g² and quartic in gauge-field strength and curvature tensor.     

Complete Gauge theory for the whole Poincaré group

Gauge theories for nonsemisimple groups are examined. A theory for the Poincaré group with all the essential characteristics of a Yang-Mills theory necessarily possesses extra equations. Inonü-Wigner contractions of gauge theories are introduced which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints.Work supported by FINEP under Contract No. B/76/80/146/00/00.Fellow of the CNPq, Brasilia.     

Polaron theory of the F-F′ conversion in alkali halides

Extending recent suggestions regarding the vibronic properties of F-centers in alkali halides, the following scenario is now proposed of the optical conversion of F-centers into F′-centers: An excited F-center electron, formed by photobleaching in the F-band, passes into a bound polaron state before passing on to an F-center to give rise to an F′-center. The detachment of the electron cloud from the excited F-center involves configurational tunneling in an exothermic process. However, both the tunneling barrier and the electron-transfer expectancy depend drastically on the host material leading to different activation energies and frequency factors of the conversion efficiency in different hosts. The Fcenter-polaron conversion is effected through the strong coupling to at least two modes, one being the LO lattice mode of the crystal. The F to F′ conversion efficiency for various hosts is calculated using a reaction-rate method and found to agree reasonably well with available experimental data.     

Limits on the mass of a superstring Z′ from the CERN pp̄ collider

We illustrate how recent CERN pp̄ collider data can be used to bound the mass of a possible Z′ in superstring-inspired models. We take into account the fact that the Z′ couplings to quarks and leptons are smaller than those of the conventional Z, and the possibility that the Z′ may be able to decay into exotic particles, thereby suppressing the Z′→ℓ⁺ℓ⁻ branching ratio. In the minimal rank-five model we find m_Z′ > 167GeV if the Z′ can only decay into conventional quarks and leptons and m_Z′ > 118 GeV for the least favourable spectrum of three E₆27 generations of particles and sparticles which is allowed by other experiments. When combined with a global analysis of neutral current data, the latter conservative limit can be increased to m_Z′ > 156 GeV. We derive analogous limits for two other superstring-inspired models. We show how these limits can be improved using future FNAL Tevatron and SLC data.     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

SU(2) ×U(1) Gauge theory of bosonic and fermionic fields inS 3 ×R space-time

The tetradic Lorentz-gauge invariant formulation of the SU(2) × U(1) theory in S³ × R space-time is presented and the general gauge covariant Dirac-Klein-Gordon-Maxwell-Yang-Mills equations are derived. A direct comparison of these equations to those of the SU(2) × U(1) gauge theory on Minkowskian background points out major differences effectively induced by the minimally coupling to S³ × R gravity.     

Comment on the quark masses in the SU(5)×U(1) model derived from the 4D fermionic superstring

In this letter, the problems of the up-quark and neutrino mass matrix, as well as the lepton non-conservation are discussed within the N=1 supersymmetric SU(5)×U(1) model derived from the four-dimensional fermionic superstring.     

Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

About the Eötvös experiment and the hypercharge theory

A careful analysis of the linear correlation between the data of the Eötvös experiment and the baryon number per unit atomic mass shows (i) that it has a positive slope and approximately goes through the origin, and (ii) that the errors are so great that it can accomodate the weak equivalence principle of general relativity as well as the hypercharge theory of Fischbach et al., both for an attractive or a repulsive force.     

Development of the Fast Ionization Gauge in a Strong Magnetic Field

The neutral gas pressure near plasma or divertor plates are very important for the plasma-wall interaction, which determines the operating mode of divertor and confining performances of plasma in tokamaks. A fast ionization gauge (fast gauge) is designed for this purpose in the HL-2A tokamak.     

Calculated conversion rate of E′4 centers into E′2 centers in alpha quartz

Recent cluster calculations by Rudha et al. [1] are used to obtain a pseudo-Jahn-Teller adiabatic energy profile for the interconversion between E′₄ centers and E′₂ centers based on the structural models proposed therein. Reasonable values are obtained for the underlying parameters which lends some further support to the models. A reaction rate method is next used to compute the temperature dependence of the conversion rate in either direction, as well as of the rate for reorientational flopping of Fowler's E′₁ center. Thermally-activated tunneling is found to be the main factor controlling the conversions in most of the temperature range of any practical interest.     

Cluster perturbation theory in Hubbard model exactly taking into account the short-range magnetic order in 2 × 2 cluster

The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 × 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.     

Gauge covariance of the Aharonov–Bohm phase in noncommutative quantum mechanics

The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a background vector potential leads to the gauge non-covariance of the phase factor. Due to this fact, the Aharonov–Bohm phase in NCQM which is evaluated through the path-integral or by shifting the coordinates is neither gauge invariant nor gauge covariant. We show that the gauge covariant Aharonov–Bohm effect should be described by using the noncommutative Wilson lines, what is consistent with the noncommutative Schrödinger equation. This approach can ultimately be used for deriving an analogue of the Dirac quantization condition for the magnetic monopole.     

The Sine-Gordon field theory model at α2=8π, the non-superrenormalizable theory

We study the Sine-Gordon field theory at ²=8. We prove that the theory is renormalizable but not superrenormalizable and we show how the perturbative renormalization procedure works in this case where the interaction is not polynomial. To go beyond the perturbative results we investigate the -functional equation for this theory and discuss in what sense at ²=8 the theory is lacking the asymptotic freedom and how it is asymptotic free for ²<8 in a appropriate region of the coupling constants.     

Use of ɛ expansions in the theory of the gravitational effect

The equations of state found by the expansion method by Brézin, Wallace, and Wilson and Avdeeva and Migdal are applied to the investigation of the gravitational effect in the critical region. As a result, expansions are obtained for the numerical coefficients in the asymptotic behaviors of the scale functions of these equations. The results of the calculation of the coefficients are compared with available experimental data for a number of liquids and magnets.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–81, May, 1980.     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.     

On the ππ-scattering lengths in the theory with effective Lagrangian

Use of the effective Lagrangian incorporating both the scalar and pseudoscalar mesons gives a possibility to calculate the ππ-scattering lengths without attraction of the ChPT theory.     

Structure of the Gauge Invariant Quark Green’s Function in QCD2

We study, in two-dimensional QCD and in the large-N _c limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered phase factor along a straight line. The analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power ?3/2, starting at positive mass squared values. Its expression is analytically determined.     

On the ε-expansion procedure in the RNG theory of turbulence

Rescaling the equations of eliminating small scales, the physical justification for the-expansion procedure in the RNG theory of turbulence is proposed, in terms of that the inertial effects are small comparing with the viscous effects at the vicinity of the Kolmogorov dissipation wavenumber.We are grateful to Professor Chao-Hao Gu for numerous helpful suggestions. We would also like to acknowledge Professor Ke-Lin Wang and Bing-Hong Wang for many stimulating discussions of these problems.