Der Grundzustand der Urfermionen im Gitterraum

The energy of the Dirac sea of interacting urfermions in a lattice space withZ ³ points is calculated using Heisenberg's Hamiltonian and a two-particle approximation which is a variational calculation with the test function ¦?〉=e ⁱη¦D ₀〉; ¦D ₀〉 is the Dirac sea without interaction,η=(ψ ^° ψ) a bilinear expression of the urfermion creation and annihilation operators. The same result is obtained by a BCS-calculation. Beyond that, we derive simple lower and upper bounds for the energy. Excited states are considered consisting of a particle-antiparticle pair with the energyE=2√ω ²+M ². The massM and the interaction constantW are connected by the equation (4W)^?1=Z ^?3∑(ω ²+M ²)^?1/2. For usual masses 4W～√Z/1 (1 a nuclear length). Methods are discussed to improve the results.     

Der Wechselwirkungsoperator im Gitterraum

In previous papers we have developed the Dirac equation in a lattice space with a finite numberZ ³ of points. This equation is quasi relativistic. For in the limitZ→∞ we obtain the relativistic energy-momentum relation. Here we derive the quasi relativistic interaction operator from a lattice space. First we prove that, without any loss of generality, the number of particles can be assumed as constant. Then we deduce an interaction operator being uniquely defined by some postulates, the most important of which are (i) the particle-hole symmetry (either the particles or the antiparticles may be considered as holes), (ii) the Racah covariance (eigenvalues are symmetrical to zero), (iii) the Touschek covariance (eigenvalues depend only on the square of the bare massκ). The other postulates are more or less obvious: 2-particle-forces, local interaction, translation invariance and cube symmetry. In the limitZ→∞ the operator is Lorentz invariant. Since the parity symmetry is broken, some alternative systems of postulates are considered. Finally we point out that the proper elementary particles are quasi particles in a certain Dirac sea of a constant number of urfermions. Essentially as inDirac's original theory of free particles the urfermions occupy half of the quantum places of the lattice. Of course, the Dirac sea now is modified by interaction.     

Über eine Näherung für Gitterelektronen in äußeren Feldern

The Hamilton operator of an electron in a periodic lattice potential under influence of external electric and magnetic fields with potentialsV(r) andA(r) resp. is often replaced by an approximate operatorW ⁰ (?i?+A(r))+V(r) for one single energy bandW ⁰(k) which means a renormalization of the kinetic energy by the lattice. The validity of this replacement is examined and the magnitude of its error is roughly estimated. Neglecting other bands one obtains an error term proportional to the derivative of the electric field strengthF, if one takes a suitable position of the “raster” of the replacement operator, and to the square of the magnetic field strengthB resp. The decoupling from the other energy bands leads to error terms proportionalF ² andB ² resp. which however in the general case increase rapidly in the vicinity of overlapping energy bands.     

Probabilities of forbidden magnetic-dipole transitions in the hydrogen atom and hydrogen-like ions

Explicit formulasfor strongly forbidden magnetic-dipole transitiions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived. The expressions for transition probabilities are presented in the form W _{n′jl; njl} ^(M1) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, and Z is the nuclear charge; the constants D _n′n ^lj are presented in an analytical form. Before now, only the D ₂₁ ^01/2 coefficient corresponding to the 1s _1/2–2s _1/2 transition was known in explicit form. The results obtained can be used in designing an experiment on parity violation in the hydrogen atom.     

Dominant decays of scalar leptoquarks and scalar gluons in the minimal four-color symmetry model

Fermionic and weak decays of the scalar leptoquarks S = S ₁ ⁽⁺⁾ , S ₁ ^(?) , and S _m and the scalar gluons F = F ₁ and F ₂ predicted by the minimal model involving four-color symmetry and the Higgs mechanism of quark-and lepton-mass splitting are considered. The widths and the branching ratios are calculated for these decays, and the results are analyzed versus the couplings and masses of decaying particles. It is shown that, at relatively small mass splittings Δm within scalar doublets (Δm < m _W), the fermionic decays S ₁ ⁽⁺⁾ → tl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → t \(\tilde \nu \) _j, F ₁ → t \(\tilde b\), and F ₂ → t \(\tilde t\), which are characterized by few-GeV widths for m _S, m _F < 1 TeV and decay branching ratios close to unity, are dominant, but that, for Δm > m _W, the weak decays S → S′W and F → F’W compete with the above fermionic decays. In the case of m _S < m _t, the processes S ₁ ⁽⁺⁾ → cl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → bl _j ⁺ , and S _m → c \(\tilde \nu \) _j, whose total branching ratios are Br(S ₁ ⁽⁺⁾ → cl ⁺) ≈ Br(S ₁ ^(?) → v \(\tilde b\)) ≈ 1, Br(S _m → bl ⁺) ≈ 0.9, and Br(S _m → c \(\tilde \nu \)) ≈ 0.1, appear to be dominant decays of scalar leptoquarks. Searches for these decays at LHC and the Tevatron are of interest.     

Long Time,Large Scale Limit of the Wigner Transform for a System of Linear Oscillators in One Dimension

We consider the long time, large scale behavior of the Wigner transform W _? (t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile et al. in Phys. Rev. Lett. 96 (2006) to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile et al. in Arch. Rat. Mech. 195(1):171–203 (2009). In the present paper we prove that in the unpinned case there exists γ ₀>0 such that for any γ∈(0,γ ₀] the weak limit of W _? (t/? ^3/2γ ,x/? ^γ ,k), as ??1, satisfies a one dimensional fractional heat equation \(\partial_{t} W(t,x)=-\hat{c}(-\partial_{x}^{2})^{3/4}W(t,x)\) with \(\hat{c}>0\). In the pinned case an analogous result can be claimed for W _? (t/? ^2γ ,x/? ^γ ,k) but the limit satisfies then the usual heat equation.     

On emission from a hydrogen-like atom

A solution of the Dirac equation for an electron in the field of a point nucleus (Ze) has been obtained as an eigenfunction of the Schrödinger Hamiltonian and the spin projection operator Σ₃. With the use of this solution, the probability W^(ν) of the emission of a neutrino per unit time from a hydrogen-like atom, \((Ze)* \to (Ze) + \nu \bar \nu\), has been calculated for the first time in the first order of the parameter Ze ? 1. The probability W^(ν) appears to be rather small, and the corresponding lifetime τ^(ν) = [W^(ν)]^–1 is much larger than the age of the Universe; correspondingly, this process cannot affect the balance of low-energy neutrinos. The smallness of W^(ν) is due not only to the presence of the obvious “weak” factor (Gm_p²)²(m/mp)⁴ in the expression for W^(ν), but also primarily to the “electromagnetic” factor (Zα)¹², which can be revealed only in a particular calculation. It has been argued within quantum electrodynamics with the mentioned wavefunctions that photon emission, (Ze)* → (Ze) + γ, can be absent (analysis of photon emission requires the further development of the method), whereas axion emission, (Ze)* → (Ze) + a, can occur, although the last two effects have not been considered in detail.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Pair production and heavy electron

Production of electron positron pairs is analysed with the hypothesis of the heavy electrone ^*. A rough agreement between theory and experiment is found if the coupling constant is suitably chosen as a function of the massm ^* of thee ^*. Comparison with upper limits for this coupling constant taken from inelastic electron proton scattering indicates that a heavy electron withm ^* between 120 MeV and 1 GeV cannot explain observed deviations from pure quantum electrodynamics.     

Localization of weakly disordered flat band states

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths ξ that diverge with a variety of unconventional exponents ν, ξ ~ 1 /W ^ν .     

Quasirelativistische Urfermionen

In recent papers we have reformulated the quantum theory of fermions in a lattice space with a finite number of points, sayZ ³. Of course, Lorentz invariance holds only in the limitZ→∞. So far a lattice space withZ ³ points provides us only with a convenient method to define the order of some limiting processes. — Here we discuss a more fundamental question. According to general relativity Lorentz invariance can not hold all over the world and must also be broken at tiny distances of the centers of particles. If the space curvature is not essential for the theory of elementary particles, as generally is assumed, we must only take into account the topological structure of the deviations from Lorentz invariance. In this respect the lattice space provides us with a rather rough but sufficient picture of a space, being approximately Lorentz invariant only for intermediate distances. — In a lattice withZ ³ points the Hilbert space has a finite number of dimensions. It seems to us important that this assumption will hold, even if we proceed to a more refined space model.     

Scattering the Geometry of Weighted Graphs

Given two weighted graphs (X, b_k, m_k), k =?1,2 with b₁ ～ b₂ and m₁ ～ m₂, we prove a weighted L¹-criterion for the existence and completeness of the wave operators W_±(H₂, H₁, I_1,2), where H_k denotes the natural Laplacian in ?²(X, m_k) w.r.t. (X, b_k, m_k) and I_1,2 the trivial identification of ?²(X, m₁) with ?²(X, m₂). In particular, this entails a general criterion for the absolutely continuous spectra of H₁ and H₂ to be equal.     

Scalar-leptoquark contributions to the neutrino magnetic moment

On the basis of astrophysical data on the neutrino magnetic moment, μ _ν < 3 × 10⁻¹² μ _B , constraints on the scalar-leptoquark masses are found within the minimal model involving four-color symmetry. It is shown that data on the neutrino magnetic moment are compatible with the mixing-parameter range that admits the existence of scalar leptoquarks whose masses are below 1 TeV, reaching experimental limits obtained from direct searches. In the case of mass degeneracy for the scalar leptoquarks S _m of electric charge Q = 2/3, the constraint m _{S m} > 330 GeV is obtained, which is independent of the mixing parameters of the model. The results are compared with the predictions of other leptoquark models. Original Russian Text ? A.V. Povarov, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 5, pp. 905–911.     

Dynamic scaling behaviors of the restricted-solid-on-solid model on honeycomb and square-octagon lattice substrates

The dynamic scaling behaviors of the restricted-solid-on-solid (RSOS) model on two new types of substrate, which are honeycomb and square-octagon lattice substrates, are studied by means of Kinetic Monte Carlo simulations. The growth exponent β and the roughness exponent α defined, respectively, by the surface width via W ~ t ^β and the saturated width via W _sat ~ L ^α , L being the system size, were obtained by a power-counting analysis. Our simulation results show that the Family-Vicsek scaling is still satisfied. However, the structures of the substrates indeed affect the dynamic behavior of the growth model. The values of the roughness exponents fall between regular and fractal lattices. Deeper analysis show that the coordination number of the substrates play an crucial role.     

Contribution of the charged Higgs boson to the production of a <Emphasis Type="Italic">tb</Emphasis> pair in hadron collisions

The contribution of the charged Higgs boson to the production of a tb pair in pp collisions at LHC is investigated. It is shown that, due to H^±-boson exchange, the total yield of tb pairs is modified significantly for small and large values of tan β. At small values of tan β, the production of right-handed t quarks is also expected, however, in contrast to what occurs in the case of only W^±-boson exchange, generating left-handed t quarks exclusively. This fact provides the possibility of separating the H^± and W^± contributions by investigating the angular distributions of products originating from top-quark decay. A detailed simulation of signal and relevant background processes is performed.     

Field-theory methods in coagulation theory

Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = {n ₁, n ₂, ..., n _g , ...}, where n _g is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W(Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.     

On coding of a quantum source of states with a finite frequency band: Quantum analogue of the Kotel’nikov theorem on sampling

An example of coding a source of quantum states with a finite frequency band W and finite exit power not exceeding ～(?W)W is given. The number of classical information bits that can be coded in the quantum states generated by such a source per unit time is C=W. Such a source is minimal in the sense that the filling factor for each of the orthogonal single-particle modes constituting N=WT-photon vector in time window 2T is equal to 1. This result can be treated as a quantum analogue of the Kotel’nikov theorem on sampling for classical signals     

Stability of Coulomb systems

The stability of m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? Coulomb systems formed by particles of unit charge against dissociation is considered as a function of the particle mass. It is shown that, from the stability of the m ₁ ⁺ m ₂ ⁺ m ₃ ^? three-particle system, it follows that the m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? four-particle system containing an additional particle of mass satisfying the condition m ₄ ^? ? m ₃ ^? is stable. The results of calculations of the stability domain for m ₁ ⁺ m ₂ ⁺ m ₃ ^? systems asymmetric in particle masses are reported. The stability of 39 asymmetric exotic four-particle molecules and mesic molecules against dissociation is established.     

Model-independent analysis of <Emphasis Type="Italic">CP</Emphasis> violation effects in decays of the Higgs boson into a Pair of the <Emphasis Type="Italic">W</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> bosons

Effects of CP and T invariance violation are studied in the most general interaction of the Higgs boson with the intermediate vector W ^± and Z bosons. Various angular distributions of the cascade decay Φ → W ⁺ W ^?/ZZ → 4 of fermions in the transversity and helicity systems are calculated, and asymmetries are constructed and evaluated. It is shown that studying the azimuthal angle distribution of the process Φ → ZZ → (e ^? e ⁺)(μ^?μ⁺) in the transversity system is effective for measuring the spatial parity of the Higgs boson.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.