Regular Series


Vol. 29 (1998), No. 3, pp. 513 – 822


Diffusion in Periodic Potential Langevin versus Fokker–Planck Equation Approach

abstract

Phonon activated diffusion of an interstitial impurity in one dimensional cosine potential is discussed with the use both of Langevin (continuous diffusion model) and Fokker–Planck (jump-diffusion model) equations. Jump rate, jump length and diffusion coefficient as a function of temperature at various barrier heights are calculated. There is some difference between results provided by these two models. Therefore the question arises to what extend these two models of diffusion are equivalent.


Back Reaction on the Metric. Beyond the Page Approximation

abstract

The back reaction of the quantized conformal massless scalar field in the Hartle–Hawking state upon the Schwarzschild geometry is considered perturbatively. Recently proposed approximation of the renormalized stress-energy tensor, which is known to properly reproduce exact numerical calculations, is used as the source term in the semi classical Einstein equations. The nature of the resulting spherically-symmetric and static metric is studied through the construction of the effective potential for null and timelike circular orbits and the analysis of the corrections to the trace anomaly. The modifications caused by the back reaction on the temperature and entropy are analysed.


Geometry Associated with Self-Dual Yang–Mills and the Chiral Model Approaches to Self-Dual Gravity

abstract

A geometric formulation of the Moyal deformation for the self-dual Yang–Mills theory and the Chiral Model approach to self-dual gravity is given. We find in Fedosov’s geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of the six-dimensional version of the second heavenly equation and the Park–Husain heavenly equation. The Wess–Zumino–Witten-like Lagrangian of self-dual gravity is reexamined within this context.


Lattice Models of Random Geometries

abstract

We review models of random geometries based on the dynamical lattice approach. We discuss one dimensional model of simplicial complexes (branched polymers), two dimensional model of dynamical triangulations and four dimensional model of simplicial gravity.


Gauge Transformations for Self/Anti-Self Charge Conjugate States

abstract

Gauge transformations of type-II spinors are considered in the Majorana–Ahluwalia construct for self/anti-self charge conjugate states. Some speculations on the relations of this model with the earlier ones are given.


Texture Dynamics for Neutrinos

abstract

An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation) \( m_\tau \simeq 1776.80 \) MeV from the experimental values of \( m_e \) and \( m_\mu \), in agreement with \( m_\tau ^{\rm exp} = 1777.00^{+0.30}_{-0.27} \) MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations \(\nu _\mu \rightarrow \nu _\tau \) is \(\sim 1/2 \) and \(|m^2_{\nu _\tau } -m^2_{\nu _\mu }| \sim (0.0003\;{\rm to}\;0.01)\;\,{\rm eV}^2\), as seems to follow from atmospheric-neutrino experiments, this ansatz predicts \( m_{\nu _e} \ll m_{\nu _\mu } \sim (0.2\;\,{\rm to}\;\,1)\times 10^{-2} \) eV and \( m_{\nu _\tau } \sim (0.2\;\,{\rm to} \;\,1)\times 10^{-1}\;\,{\rm eV}\), and also the amplitude of neutrino oscillations \(\nu _e \rightarrow \nu _\mu \sim 2^{+4}_{-2}\times 10^{-4}\) (in the vacuum). Such a very small amplitude for \(\nu _e \rightarrow \nu _\mu \) is implied by the value of \( m_\tau ^{\rm exp} - 1776.80 \) MeV used to determine the deviation of the diagonalizing matrix \(\widehat {U}^{(e)}\) from \(\widehat {1}\) in the lepton Cabibbo–Kobayashi–Maskawa matrix \(\widehat {V} = \widehat {U}^{(\nu )\,\dagger }\widehat {U}^{(e)}\). Here, \(\widehat {U}^{(\nu )}\) by itself gives practically no oscillations \(\nu _e \rightarrow \nu _\mu \), while it provides the large oscillations \(\nu _\mu \rightarrow \nu _\tau \) .


Shadowing of Virtual Photons in Nuclei at Small \(x_{\rm Bj}\) in the QCD Dipole Picture

abstract

Compact and well defined formulae for the shadow of the virtual photon interacting with a large nucleus at small \(x_{\rm Bj}\) are given in the QCD dipole picture. Two classes of contributions are considered: (a) quasi-elastic interaction of the \(q\bar {q}\) dipole and (b) multi-pomeron coupling.


Bondi Mass in Classical Field Theory

abstract

We discuss three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. Certain generating formula on a hyperboloid and on a null surface are derived for them. The linearized Einstein equations are analyzed around the null infinity. It is shown how the dynamics can be reduced to gauge invariant quanitities in a quasi-local way. The quasi-local gauge-invariant “density” of the Hamiltonian is derived on the hyperboloid and on the future null infinity \(\cal {J}^+\). The result gives a new interpretation of the Bondi mass loss formula. We show also how to define the angular momentum. Starting from an affine approach for Einstein equations we obtain variational formulae for Bondi-Sachs type metrics related to energy and angular momentum generators. The original van der Burg asymptotic hierarchy is revisited and the relations between linearized and asymptotic nonlinear situations are established. We discuss also supertranslations, Newman-Penrose charges and Janis solutions.


Problems with Proton in the QCD Dipole Picture

abstract

The soft gluon part of a proton wave function is investigated and compared with an onium case. It is argued that at every step of the gloun cascade new color structures appear. Dipole equation kernel emerges when a diquark limit is assumed.


Proposal of Unified Fermion Texture

abstract

A unified form of mass matrix is proposed for neutrinos, charged leptons, up quarks and down quarks. Some constraints for the parameters involved are tentatively postulated. Then, the predictions are neatly consistent with available experimental data. Among the predictions are: (i) \( m_\tau \simeq 1776.80 \) MeV (with the inputs of \( m_e \) and \( m_\mu \)), (ii) \( m_{\nu _0} \ll m_{\nu _1} \sim (0.6\;\,{\rm to}\;\,4)\times 10^{-2}\,\)eV and \( m_{\nu _2} \sim (0.2\;\,{\rm to}\;\,1)\times 10^{-1}\,\)eV (with the atmospheric-neutrino inputs of \( |m_{\nu _2}^2 - m_{\nu _1}^2| \sim (0.0003\;\,{\rm to}\;\,0.01)\,{\rm eV} ^2 \) and the \(\nu _\mu \rightarrow \nu _\tau \) oscillation amplitude \(\sim 0.8 \)), and also (iii) \( m_s \simeq 270\;{\rm MeV}\), \(|V_{ub}/V_{cb}| \simeq 0.082 \) and arg\(V_{ub} \simeq -64^\circ \) (with the inputs of \( m_c = 1.3 \) GeV, \( m_b = 4.5 \) GeV, \(|V_{us}| = 0.221 \) and \(|V_{cb}| = 0.041 \), where \( m_u \ll m_c \ll m_t \) and \( m_d \ll m_s \ll m_b \)). All elements of the Cabibbo–Kobayashi–Masakawa matrix are evaluated. All elements of its lepton counterpart are calculated up to an unknown phase (Appendix B). Some items related to dynamical aspects of the proposed fermion “texture” are briefly commented on (Appendix A). In particular, the notion of a novel dark matter, free of any Standard Model interactions (and their supersymmetric variants), appears in the case of preon option.


Two Component Theory and Electron Magnetic Moment

abstract

The two-component formulation of quantum electrodynamics is studied. The relation with the usual Dirac formulation is exhibited, and the Feynman rules for the two-component form of the theory are presented in terms of familiar objects. The transformation from the Dirac theory to the two-component theory is quite amusing, involving Faddeev-Popov ghost loops of a fermion type with bose statistics. The introduction of an anomalous magnetic moment in the two-component formalism is simple; it is not equivalent to a Pauli term in the Dirac formulation. Such an anomalous magnetic moment appears not to destroy the renormalizability of the theory but violates unitarity.


Effects of the Pion Wave Distortion on the Absorption/Emission Mechanism of the DCX Reaction on \(^{56}\)Fe

abstract

We have studied the effects of pion wave-function distortion on the absorption/emission mechanism cross-section of the pionic double charge exchange reaction on \(^{56}{Fe}\). We are using pion-nucleus optical potential and quasiparticle proton–neutron random phase approximation formalisms. We confirm the resonant behaviour of the foward cross-section at around \(50\) MeV, opposite to the plane wave-function results.


Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson

abstract

We study the equation of state (EOS) of \(\beta \)-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the \(\delta \)-meson [\(a_0(980)\)]. A range of values of the \(\delta \)-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, \(E_s \approx 30\) MeV. We find that the quantity most sensitive to the \(\delta \)-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the \(\delta \)-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger \(\delta \)-meson coupling.


top

ver. 2024.03.17 • we use cookies and MathJax