The finite temperature renormalization group equation in λφ4 theory

The renormalization group equation at finite temperature is studied in the context of λφ⁴ theory. Three methods of deriving the finite temperature renormalization group equations are presented. The result shows that the effective mass becomes large as the temperature increases while the effective coupling constant becomes small.     

An unusual cosmological solution for λφ4 theory with broken symmetry

A particular solution to the Einstein equations is presented for an isotropic, spatially homogeneous and spatially flat space-time in the case that the matter field is that of a simple scalar ⁴ theory. The solution possesses unusual properties.     

Derivation of the polyakov string theory from planar φ3 field theory

A rigorous derivation is given of the Polyakov surface theory by summing over all planar Feynman graphs of a φ³ scalar field theory. It uses a discretization of surfaces through the triangulation induced by the dual graphs of the Feynman graphs. No approximation is made for the propagators and the metric is shown to be locally defined. The Green's functions of both theories are shown to coincide for any finite external momenta.     

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.     

Renormalizability of φ3 theory in 6-dimensional curved spacetime

We show that φ³ theory in a general 6-dimensional curved spacetime is renormalizable at the two-loop level by demonstrating the cancellation of non-local divergences. We also calculate the full set of local two-loop counterterms. The heat kernel is used to obtain an expansion for the propagator, in the presence of the background field, in configuration space. This expansion isolates singular terms in the short-distance limit which give rise to ultraviolet divergences.     

Exact combinatorics of Bern-Kosower-type amplitudes for two-loop φ3 theory

Counting the contribution rate of a world-line formula to Feynman diagrams in (φ³ theory, we explain the idea of how to determine precise combinatorics of Bern-Kosower-like amplitudes derived from a bosonic string theory for N-point two-loop Feynman amplitudes. In this connection we also present a method to derive simple and compact world-line forms for the effective action.     

Surface rumpling of cubic CaTiO3 from density functional theory

In this paper, the structure of cubic CaTiO3 （001） surfaces with CaO and TiO2 terminations has been studied from density functional calculations. It has been found that the Ca atom has the largest relaxation for both kinds of terminations, and the rumpling of the CaO-terminated surface is much larger than that of TiO2-terminated surface. Also we have found that the metal atom relaxes much more prominently than the O atom does in each layer. The CaO-terminated surface is slightly more energetically favourahle than the TiO2-terminated surface from the analysis of the calculated surface energy.     

Microscopic theory of electron-phonon interaction and superconductivity of BaPb1−xBixO3

Electron-phonon coupling coefficients in BaPb_1−xBi_xO₃ are calculated microscopically on the basis of the tight-binding band model which utilizes energy band structures obtained with the use of the self-consistent LAPW method by Mattheiss and Hamann. Assuming the rigid-band model we calculate, as a function of Bi concentration x, the dimension-l less electron-phonon coupling constant λ in McMillan's strong-coupling theory of superconductor. We obtain large values of λ such as λ>1 for x>0.1. The origin of this large electron-phonon coupling is ascribed to: (i) the hybridization between 2pσ orbitals of 0 atoms and 6s orbitals of Pb or Bi atoms is large in the conduction band, (ii) this σ-bonding is strongly affected by a vibrational motion of 0 atoms in the direction connecting the 0 and Pb (Bi) atoms, and (iii) the mass of 0 atoms is light. We also evaluate superconducting transition temperature T_c as a function of x on the basis of the McMillan-Allen-Dynes equation. The results explain semi-quantitatively the observed x-dependence of T_c.     

EFFECTIVE POTENTIAL OF λφ41+3 AT ZERO AND FINITE TEMPERATURES

The effective potential of $\lambda$$\varphi$⁴₁₊₃ model with both signs of parameter m² is evaluated at T=0 by means of a simple but effective method for regularization and renormalization. Then at T≠0, the effective potential is evaluated in imaginary time Green function approach, using the Plana formula. A critical temperature for restoration of symmetry breaking in the standard model of particle physics is estimated to be T_c≌510 GeV.     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

Summation of divergent series and Zeldovich’s regularization method

A method for summing divergent series, including perturbation-theory series, is considered. This method is an analog of Zeldovich’s regularization method in the theory of quasistationary states. It is shown that the method in question is more powerful than the well-known Abel and Borel methods, but that it is compatible with them (that is, it leads to the same value for the sum of a series). The constraints on the parameter domain that arise upon the removal of the regularization of divergent integrals by this method are discussed. The dynamical Stark shifts and widths of loosely bound s states in the field of a circularly polarized electromagnetic wave are calculated at various values of the Keldysh adiabaticity parameter and the multiquantum parameter.     

BRST invariant PV regularization of SUSY Yang–Mills and SUGRA

Pauli?CVillars regularization of Yang?CMills theories and of supergravity theories is outlined, with an emphasis on BRST invariance. Applications to phenomenology and the anomaly structure of supergravity are discussed.     

Many-body theory of π electron systems

Many-body perturbation theory is developed within the dielectric function method presented in a preceding paper [15]. We have explicitly considered the local field corrections (which are disregarded in the random phase approximation) to the self consistent field. These corrections are of second order in the density-density correlation function x and are evaluated exactly in the framework of the adopted approximation scheme because all the integrals which appear in the expressions can be evaluated analytically. Here the method is applied to π electron systems within the zero differential overlap approximation ; explicit calculations of the excitation energies of the benzene molecule using different parametrizations are presented. Comparison is made with results obtained in the RPA and other schemes.     

Semi-gross theory of nuclear β-decay

The gross theory of β-decay is refined to take into account shell effects of the parent nuclei, and the resulting theory is named semi-gross theory. In this theory, the one-particle energy distribution in the parent nucleus is taken to have structures, and the one-particle strength function is assumed to depend on the quantum numbers of the initial state of the decaying nucleon. β-decay (partial) half-lives are calculated for 1659 nuclides, and the results are compared with experimental data as well as with those calculated by the gross theory. The β-decay strength functions are shown for two selected nuclides, and briefly discussed. These numerical studies confirm that the semi-gross theory includes some part of the shell effects correctly, although there still remain deviations of the theoretical results from experimental data, which should, at least partly, be due to shell effects of the daughter nuclei. Comparison of the present results with microscopic theories shows that the overall accuracy of the semi-gross theory is comparable with those of the microscopic theories.     

Precision frequency measurement of ~1S_0–~3P_1 intercombination lines of Sr isotopes

We report on frequency measurement of the intercombination(5s2)1S0–(5s5p)3P1transition of the four natural isotopes of strontium,including88Sr(82.58%),87Sr(7.0%),86Sr(9.86%),and84Sr(0.56%).A narrow-linewidth laser that is locked to an ultra-low expansion(ULE)optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10-13at an integration time of 1 s.The fluorescence collector and detector are specially designed,based on a thermal atomic beam.Using a double-pass acousto-optic modulator(AOM)combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines,which allows us to determine the transition frequency precisely.The optical frequency is measured using an optical frequency synthesizer referenced to an H maser.Both the statistical values and the final values,including the corrections and uncertainties,are derived for a comparison with the values given in other works.     

Application of the probability theory in predicting 3D focusing behaviors of compound X-ray refractive lenses

X-rays promise a high resolving power due to the veryshort wavelength. Therefore, people have been trying todevelop X-ray optical devices for focusing X-ray beam toa small spot to perform X-ray analysis techniques. In1996, Snigirev et al.[1] proposed and demonstrated thatX-ray refractive focusing could be accomplished with acompound X-ray refractive lens (CRL). And then manypublications on the further researches appeared[2-8]. Thetheoretical results on the focusing performances in the fo-c…     

Electronic structure and optical properties of In-doped SrTiO3 by density function theory

The effect of In doping on the electronic structure and optical properties of SrTiO3 is investigated by the first-principles calculation of plane wave ultra-soft pseudo-potential based on the density function theory （DFT）. The calculated results reveal that due to the hole doping, the Fermi level shifts into valence bands （VBs） for SrTi1-x InxO3 with x = 0.125 and the system exhibits p-type degenerate semiconductor features. It is suggested according to the density of states （DOS） of SrTi0.875In0.125O3 that the band structure of p-type SrTIO3 can be described by a rigid band model. At the same time, the DOS shifts towards high energies and the optical band gap is broadened. The wide band gap, small transition probability and weak absorption due to the low partial density of states （PDOS） of impurity in the Fermi level result in the optical transparency of the film. The optical transmittance of In doped SrTiO3 is higher than 85% in a visible region, and the transmittance improves greatly. And the cut-off wavelength shifts into a blue-light region with the increase of In doping concentration.     

Non-linear theory of vibration and aesthetics of raga music

The non-linear theory of vibration has recently been applied toa number of problems in physics and was found to give many interestingresults which were absent in the case of linear vibration.It is natural tothink of the outcome of application of non-linear theory to raga music,atopic which has hitherto been unexplored.It has been found that a newrealm of musical idea is obtained if one considers the effects ofnon-linearity in physics on the understanding of the aesthetics and beautyin raga music when two notes are sounded simultaneously.