abstract

In a recent letter by H. Davoudiasl, R. Kitano, T. Li and H. Murayama “The new Minimal Standard Model” (NMSM) was constructed which incorporates new physics beyond the Minimal Standard Model (MSM) of particle physics. The authors follow the principle of minimal particle content and therefore adopt the viewpoint of particle physicists. It is shown that a generalisation of the geometric structure of spacetime can also be used to explain physics beyond the MSM. It is explicitly shown that for example inflation, i.e.  an exponentially expanding universe, can easily be explained within the framework of Einstein–Cartan theory.

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The oscillator algebra of Pegg–Barnett (P–B) oscillator with a finite-dimensional number-state space is considered. It is found that such a finite-dimensional oscillator possesses an su(\(n\)) Lie algebraic structure. A so-called supersymmetric P–B oscillator is suggested, and some related topics (such as the algebraic structure and the occupation number operator of the supersymmetric P–B oscillator) are briefly discussed. In addition, as one of the applications of the P–B quantization, a potential formula for the masses of charged leptons, which agrees reasonably well with the experimental values, is constructed based on the concept of supersymmetric P–B oscillator.

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The effect of a soft phase core appearance in the center of polytropic star is analyzed by means of linear response theory. Approximate formulae for the changes of radius, moment of inertia and mass-energy of non-rotating configuration with arbitrary adiabatic indices are presented, followed by an example evaluation of astrophysical observables.

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Wir charakterisieren die Darstellungen \({\mit \Gamma }\) einer halbeinfachen Lie- Algebra \(\frak {s}\), die mit einer \((2N+1)\)-dimensionalen Heisenberg-Algebra \(\frak {h}_{N}\) verträglich sind, d.h., für die es eine unzerlegbare Lie-Algebra mit der Levi-Zerlegung \(\frak {s}\overrightarrow {\oplus }_{{\mit \Gamma }}\frak {h}_{N}\) gibt. Besonders wird die enge Beziehung zwischen solchen irreduziblen selbstadjungierten Darstellungen und die Klassifikation reeller Darstellungen einer Lie-Algebra beobachtet. Weiter wird die Anzahl der Casimiroperatoren der Algebren \(\frak {s}\overrightarrow {\oplus }_{{\mit \Gamma }}\frak {h}_{N}\) sowie etlicher ihrer inhomogenen Kontraktionen analysiert, und es werden verbesserte Schranken für die Invariantenzahl der Lie-Algebren \(\frak {s}\overrightarrow {\oplus }_ {{\mit \Gamma }}\dim {\mit \Gamma } L_{1}\) mit abelschem Radikal erhalten. Die Struktur verträglicher Darstellungen wird im letzten Teil auf die Theorie induzierter Darstellungen angewandt.

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“No one has ever touched Zeno without refuting him”. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his famous paradoxes of motion. Reflections on continuity of space and time lead us to Banach and Tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes. Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental facts. Then we discuss supertasks and bifurcated supertasks. The concept of localisation leads us to Newton and Wigner and to interesting phenomenon of quantum revivals. At last we note that the paradoxical idea of timeless universe, defended by Zeno and Parmenides at ancient times, is still alive in quantum gravity. The list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.

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There exists a scenario of a proof of the general Penrose inequality that requires a convexity property and the no-twist condition of a foliation of the Cauchy hypersurface. This paper shows that the no-twist condition can be removed and that, in the Schwarzschild geometry with linear axial perturbations, there do exist foliations that are convex in the required sense.

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In this paper we present our partial results of numerical investigation of the quantum Coulomb field \(|u\rangle \). In particular we investigate the matrix of the \(C_1=-1/2 M_{\mu \nu } M^{\mu \nu }\) operator in Jacobi base, obtained from orthonormalization of \(C_1^n|u\rangle \) vectors and photon distribution in the bound state of the \(C_1\) operator, in search for some critical values of the coupling constant \(e^2\) of the theory. So far our results are negative, that is, all characteristics we studied are smooth functions of \(0\lt e^2\lt \pi \).

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We study the decay widths of the processes \(H^+\rightarrow W^+\, H^0\, (h^0,A^0)\), including the Lorentz violating effects and analyze the possible CPT violating asymmetry arising from CPT odd coefficients. We observe that these effects are too small to be detected, since the corresponding coefficients are highly suppressed at the low energy scale.

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The entropy properties are analyzed by Ma’s coincidence method in \(\pi ^{+}p\) and \(K^{+}p\) collisions of the NA22 experiment at 250 GeV/\(c\) incident momentum. By using the Rényi entropies, we test the scaling law and additivity properties in rapidity space. The behavior of the Rényi entropies as a function of the average number of particles is investigated. The results are compared with those from the PYTHIA Monte Carlo event generator.

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We revisit the challenging problem of finding an efficient Monte Carlo (MC) algorithm solving the constrained evolution equations for the initial-state QCD radiation. The type of the parton (quark, gluon) and the energy fraction \(x\) of the parton exiting emission chain (entering hard process) are predefined, i.e. constrained throughout the evolution. Such a constraint is mandatory for any realistic MC for the initial state QCD parton shower. We add one important condition: the MC algorithm must not require the a priori knowledge of the full numerical exact solutions of the evolution equations, as is the case in the popular “Markovian MC for backward evolution”. Our aim is to find at least one solution of this problem that would function in practice. Finding such a solution seems to be definitely within the reach of the currently available computer CPUs and the sophistication of the modern MC techniques. We describe in this work the first example of an efficient solution of this kind. Its numerical implementation is still restricted to the pure gluon-strahlung. As expected, it is not in the class of the so-called Markovian MCs. For this reason we refer to it as belonging to a class of non-Markovian MCs. We show that numerical results of our new MC algorithm agree very well (to \(0.2\%\)) with the results of the other MC program of our own (unconstrained Markovian) and another non-MC program QCDnum16. This provides a proof of the existence of the new class of MC techniques, to be exploited in the precision perturbative QCD calculations for the Large Hadron Collider.

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We solve the LO DGLAP QCD evolution equation for truncated Mellin moments of the nucleon nonsinglet structure function. The results are compared with those, obtained in the Chebyshev-polynomial approach for \(x\)-space solutions. Computations are performed for a wide range of the truncation point \(10^{-5}\leq x_0\leq 0.9\) and \(1\leq Q^2\leq 100~{\rm GeV}^2\). The agreement is perfect for higher moments (\(n\geq 2\)) and not too large \(x_0\) (\(x_0\leq 0.1\)), even for a small number of terms in the truncated series (\(M=4\)). The accuracy of the truncated moments method increases for larger \(M\) and decreases very slowly with increasing \(Q^2\). For \(M=30\) the relative error in a case of the first moment at \(x_0\leq 0.1\) and \(Q^2=10~{\rm GeV}^2\) does not exceed 5% independently on the shape of the input parametrisation. This is a quite satisfactory result. Using the truncated moments approach one can avoid uncertainties from the unmeasurable \(x\rightarrow 0\) region and also study scaling violations without making any assumption on the shape of input parametrisation of parton distributions. Therefore the method of truncated moments seems to be a useful tool in further QCD analyses.

abstract

The multistep direct reaction theory of Feshbach, Kerman and Koonin (FKK) is used with the enhanced non-DWBA matrix elements and with both the coherent vibrations and the incoherent particle–hole excitations, included. Distinction between bound and unbound final particle–hole states is made, since only the former determine genuine one-step cross sections that observe the energy weighted sum rule limits and can be convoluted to obtain the multistep cross sections for emission of one particle. The cross sections to unbound final states describe more complicated direct processes. Only the very specific of such processes can be evaluated in terms of the FKK theory. These novelties are verified in analyses of a representative series of reactions.

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The previously derived expressions for the real part of the single particle potential of a \({\mit \Sigma }\) hyperon in nuclear matter, \(V_{\mit \Sigma }\), are applied to investigate the dependence of \(V_{\mit \Sigma }\) on the nuclear matter density and \({\mit \Sigma }\) momentum. Results for \(V_{\mit \Sigma }\), in particular its isospin, spin, and spin-isospin dependent parts, obtained for four models of the Nijmegen baryon–baryon interaction are presented and discussed.

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The dependence of the size of the thermal source on centrality in ultrarelativistic heavy-ion collisions is studied. The interaction region consists of a well defined thermalized core, and of an outer mantle where the production scales with the number of participants. The thermal source builds up in the region with the largest density of participants in the transverse plane. Particle production in the thermalized core is enhanced in comparison to the wounded nucleon model. The change of the degree of strangeness saturation with centrality is also discussed. We perform an estimate of high \(p_\perp \) jet absorption finding that an increase of the absorption in the thermal core is compatible with the data.

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A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the finite volume of the system. A complete analysis of the isobaric partition singularities is done for finite system volumes. The finite size effects for large fragments and the role of metastable (unstable) states are discussed. These results allow us, for the first time, to exactly describe the finite volume analog of the bulk nuclear liquid phase and understand completely its contribution to the grand canonical partition.

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A simple phenomenological formula for description of \(\alpha \)-decay half-lives \(T_{\alpha }\) of heavy (above \(^{208}\)Pb) and superheavy nuclei is proposed. The formula, expressing \(T_{\alpha }\) as a function of the decay energy \(Q_{\alpha }\), has five adjustable parameters: three to describe even–even nuclei and two for accounting for effects of an odd proton and an odd neutron. The formula allows one to describe measured values of \(T_{\alpha }\) of 61 even–even nuclei roughly within a factor of 1.3, 45 odd–even nuclei within a factor of 2.1, 55 even–odd nuclei within a factor of 3.2 and 40 odd–odd nuclei within a factor of 4.0, on the average, when measured values of \(Q_{\alpha }\) are taken. Results of its use are compared with those of other formulae. Effects of various changes in the formula are discussed.

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It is pointed out that the moments of phase-space particle density at freeze-out can be determined from the coincidence probabilities of the events observed in multiparticle production. A method to measure the coincidence probabilities is described and its validity examined.

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Neutron one-quasiparticle states of heaviest nuclei are calculated within a macroscopic–microscopic approach. Basic characteristics of these states (projection of spin on the symmetry axis, parity, excitation energy, Nilsson label) are given. Much attention is paid to systematics of them (especially of the ground state), as functions of proton number. Other important properties of the analyzed nuclei, as deformation, deformation energy, shell correction to energy and neutron pairing-energy gap parameter, are also given. Heavy and superheavy (even-\(Z\), odd-\(N\)) nuclei with proton number \(Z=90\)–110 and neutron number \(N\)=145–161 are considered. All of them are expected to be deformed. It is obtained that characteristics of the ground states, which are known experimentally, is rather well reproduced.

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Theories of fundamental physics as well as cosmology must ultimately not only account for the structure and evolution of the universe and the physics of fundamental interactions, but also lead to an understanding of why this particular universe follows the physics that it does. Such theories must ultimately lead to an understanding of the values of the fundamental constants themselves. However, all such efforts have failed, leaving fundamental constants outside of any physical theories. In this paper we take a different approach than the usual evolutionary picture where the physics itself is assumed invariant. We study numerical relations among fundamental constants starting from relationships first proposed by Weinberg. We have shown that they turn out to be equivalent to the relations found by Dirac. Then a new scaling hypothesis relating the speed of light \(c\) and the scale of the universe \(R\) is explored. The “coincidences” of Dirac and Eddington concerning large numbers and ratios of fundamental constants do not need to be explained in our view, rather they are accepted as premises and in the process, they yield a fundamentally different view of the cosmos. We develop an axiomatic approach and the fundamental constants can be assumed to vary and this variation leads to an apparent expansion of the universe. Also the variation of constants leads to change in the parameters like permittivity and refractive index of the quantum vacuum. This gives rise to a possibility of explaining some of anomalies found in the observations of high redshift quasars. The variations of the fundamental constants lead to a changing universe, i.e. , the number of nucleons varies, etc. The increase of the number of nucleons and the redshift of the spectral lines appear to be related to the emergence of an arrow of time as perceived by an observer in the present universe. Possible implications of this new approach in astrophysical domains are discussed.

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We present a simple Onsager type density functional theory (DFT) of a two-dimensional system of hard needles and assume that it can be applied to describe intensive and short range properties of a real system which, on the other hand, on larger scales exhibits topological order. It is shown that the transition point of the isotropic-nematic transformation and the state equation obtained are almost the same as those predicted from the computer simulations [Phys. Rev. A31, 1776 (1985)] for small and undistorted system, which is never the case in liquid crystals, where these results are shifted in the density and require rescalings like, for instance, the Parson–Lee approach [Phys. Rev. A19, 1225 (1979); J. Chem. Phys. 87, 4972 (1987); J. Chem. Phys. 89, 7036 (1988).] Similar effect occurs for the chemical potential. Such behavior is attributed to the presence of negative values of higher virial coefficients, which may cancel the influence of the other positive coefficients in such a way that the second virial approximation gives accurate predictions. The above conclusion coincides with the Onsager idea that the second virial DFT theory for infinitely 3D hard particles is accurate. We notice that this coincidence comes from the fact that the 3D and 2D interaction models are governed by the same theoretical formulation. We also claim that the observed in the Monte Carlo simulation the disclinations unbinding process does not mean the change from the isotropic to the nematic phase (IN), as believed before, since the spontaneously drifting disclinations cannot be responsible for the changes of the system symmetry. The IN transition, as usual, is driven by the molecular interactions and the disclination unbinding must undergo then in the uniaxial phase. We also confirm that the chemical potential has a smooth character as a function of pressure, whereas it has an abrupt change in the slope at the point of transition while plotted versus density.

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This paper examines the emerging phenomenon of blogging, using three different Polish blogging services as the base of the research. Authors show that blog networks are sharing their characteristics with complex networks (\(\gamma \) coefficients, small worlds, cliques, etc.). Elements of sociometric analysis were used to prove existence of some social structures in the blog networks.