abstract

The explicit construction of states saturating uncertainty relations following from basic commutation rules of NCQM is given both in Fock space and coordinate representation.

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The complete list of Poisson–Lie structures on the Galilei group acting in 4-dimensional space–time is presented.

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The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson’s classical electron [Acta Phys. Pol. 6, 218 (1937)], further discussed by Weyssenhoff and Raabe [Acta Phys. Pol. 9, 7 (1947)]. The two-parameter centrally extended Galilean symmetry of the model is recovered using elementary methods. The relation to Schrödinger’s Zitternde Elektron is indicated.

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The (2+1) dimensional non-linear electrodynamics, the so called Pagels–Tomboulis electrodynamics, with the Chern–Simons term is considered. We obtain “generalised self-dual equation” and find the corresponding generalised massive Chern–Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained.

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For weak decays \(B_d^{0}\rightarrow \pi \pi \) and \(K\overline {K}\) the effects of SU(3) breaking in coupled-channel final-state interaction effects are discussed in a Regge framework. It is shown that SU(3) breaking in the inelastic final-state transitions dramatically affects the phases of the isospin \(I=0,1,2\) amplitudes in the \(B_d^{0}\) decays. The effect of the singlet penguin diagram on these phases is studied. Furthermore, on the example of the \(B_d^{0}\rightarrow \pi \pi \) decays, the dependence of CP asymmetries on the size of penguin amplitude is analyzed.

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Using the most general model independent form of the effective Hamiltonian the rare decay \(B_{s}\rightarrow \nu \bar {\nu }\gamma \) is studied. The sensitivity of the photon energy distribution and branching ratio to new Wilson coefficients are investigated.

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We extend the isobar model for kaon photoproduction to consider higher energy data by combining the model with a Regge approach. The extended model works nicely between threshold and 16 GeV. It is shown that model with crossing symmetric Born terms leads to a better description of experimental data. We use the model to calculate contributions of kaon channels to the Gerasimov–Drell–Hearn sum rule up to 16 GeV.

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Using the SANC system we study the one-loop electroweak standard model prediction, including virtual and real photon emissions, for the decays of on-shell vector and scalar bosons \(B \to f {\bar f} (\gamma )\), where \(B\) is a vector boson, \(Z\) or \(W\), or a Standard Model Higgs. The complete one-loop corrections and exact photon emission matrix element are taken into account. For the phase-space integration, the Monte Carlo technique is used. For \(Z\) decay the QED part of the calculation is first cross-checked with the exact one-loop QED prediction of KORALZ. For Higgs boson and \(W\) decays, a comparison is made with the approximate QED calculation of PHOTOS Monte Carlo. This provides a useful element for the evaluation of the theoretical uncertainty of PHOTOS, very interesting for its application in ongoing LEP2 and future LC and LHC phenomenology.

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Lagrangian interactions in a class of two-dimensional tensor gauge field theory are derived by means of deforming the solution to the master equation with specific cohomological techniques. Both the gauge transformations and their algebra are deformed. The gauge algebra of the coupled model is open.

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Using the recent measurement of the \({\mit \Xi } ^0 \to {\mit \Lambda } \gamma \) asymmetry as an input, we reanalyse nonleptonic and weak radiative hyperon decays in a single symmetry-based framework. In this framework the old S:P problem of nonleptonic decays is automatically resolved when the most important features of weak radiative decays are taken into account as an input. Experimental data require that symmetry between the two types of hyperon decays be imposed at the level of currents, not fields. Previously established connections between hyperon decays and nuclear parity violation imply that the conflict, originally suggested by weak radiative decays, has to surface somewhere.

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We suggest that the Large Mixing Angle MSW solar solution, whose unique physical status is confidently supported by the recent results from KamLAND experiments, gets its justification in the fermion universality, interpreted for neutrinos and charged leptons in a straightforward way, most readily in the framework of seesaw mechanism. To this end, we consider an explicit seesaw model, where Dirac and (righthanded) Majorana neutrino masses are simultaneously measurable, and both are conjectured to be proportional to charged-lepton masses. However, the LMA solar solution is also not inconsistent with the simple option, where neutrinos are Dirac particles carrying masses proportional to those of charged leptons.

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We use a simple, instanton motivated, nonlocal chiral quark model to calculate pion Generalized Distribution Amplitudes (GDAs). The nonlocality appears due to the momentum dependence of the constituent quark mass, which we take in a form of a generalized dipole formula. With this choice all calculations can be performed directly in the Minkowski space and the sensitivity to the shape of the cutoff function can be studied. We demonstrate that the model fulfills soft pion theorems both for chirally even and chirally odd GDAs. The latter cannot be derived by the methods of current algebra. Whenever possible we compare our results with the existing data. This can be done for the pion electromagnetic form factor and quark distributions as measured in the proton-pion scattering.

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In order to determine polarized parton distributions we have made a new NLO QCD fit (in \(\overline {\rm MS}\) renormalization scheme) using all experimental data on spin asymmetries measured in the deep inelastic scattering on different nucleon targets. The functional form of such densities is based on MRST2001 results for unpolarized ones. We get for polarization of quarks (at \( Q^{2}=1\, {\rm GeV^{2}}\)): \(\Delta u = 0.86 , \Delta d= -0.37, \Delta s= -0.04\). The total quark polarization is rather big and we obtain: \(\Delta {\mit \Sigma }=0.45\). As a result of our fit we get \(a_{3} \cong g_{A}=1.23\), the value which is close to the experimental number. With negligible \(\Delta s\) and rather big \(\Delta {\mit \Sigma }\) (comparable to \(a_{8}\)) the results of our new fit are quite different in character from previous fits.

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A simple model, based on the analytical formula for the Compton scattering, is proposed to describe the realistic photon-energy spectra for the Photon Collider at TESLA. Parameters of the model are obtained from the full simulation of the beam by V. Telnov, which includes nonlinear corrections and contributions of higher order processes. Photon energy distribution and polarization, in the high energy part of the spectra, are well reproduced. Our model can be used for a Monte Carlo simulation of gamma-gamma events at various energies and for direct cross-section calculations.

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We calculate the self-consistent in-medium \(T\)-matrix for symmetric nuclear matter using realistic interactions with many partial waves. We find for the interactions used (CDBonn and Nijmegen) very similar results for on-shell quantities. The effective mass and the renormalization factor \(Z_{\rm F}\) at the Fermi momentum are given for a range of densities.

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We study the fourth-order squeezing in the most general case of superposition of two coherent states by considering \(\left \langle \psi \right |(\Delta X_\theta )^4\left | \psi \right \rangle \) where \(X_{\theta }= X_{1}\cos \theta + X_{2}\sin \theta ,\; X_{1 }+ iX_{2 }= a\) is annihilation operator, \(\theta \) is real, \(\left | \psi \right \rangle = Z_1 \left | \alpha \right \rangle + Z_2 \left | \beta \right \rangle \), \(\left | \alpha \right \rangle \) and \(\left |\beta \right \rangle \) are coherent states and \(Z_{1},\; Z_{2},\; \alpha ,\;\beta \) are complex numbers. We find the absolute minimum value 0.050693 for an infinite combinations with \(\alpha - \beta =1.30848 \exp [\pm i(\pi /2) + i\theta \)], \(Z_{1}/Z_{2} = \exp (\alpha ^{\ast }\beta - \alpha \beta ^{\ast })\) with arbitrary values of \(\alpha + \beta \) and \(\theta \). For this minimum value of \(\left \langle \psi \right |(\Delta X_\theta )^4\left | \psi \right \rangle \), the expectation value of photon number can vary from the minimum value 0.36084 (for \(\alpha +\beta = 0\)) to infinity. We note that the variation of \(\left \langle \psi \right |(\Delta X_\theta )^4\left | \psi \right \rangle \) near the absolute minimum is less flat when the expectation value of photon number is larger. Thus the fourth-order squeezing can be observed at large intensities also, but settings of the parameters become more demanding.

abstract

Melanins are a group of complex pigments of biological origin, widely spread in all species from fungi to man. Among diverse types of melanins, the human melanins, eumelanins, are brown or black nitrogen-containing pigments, mostly known for their photoprotective properties in human skin. We have undertaken theoretical studies aimed to understand absorption spectra of eumelanins and their chemical precursors. The structure of the biopigment is poorly defined, although it is believed to be composed of cross-linked heteropolymers based on indolequinones. As a basic model of the eumelanin structure, we have chosen pentamers containing hydroquinones (HQ) and/or 5,6-indolequinones (IQ) and/or semiquinones (SQ) often listed as structural melanin monomers. The eumelanin oligomers have been constructed as random compositions of basic monomers and optimized for the energy of bonding. Absorption spectra of model assemblies have been calculated within the semiempirical intermediate neglect of differential overlap (INDO) approximation. Model spectrum of eumelanin has been further obtained by sum of independent spectra of singular polymers. By comparison with experimental data it is shown that the INDO/CI method manages to reproduce well characteristic properties of experimental spectrum of synthetic eumelanins.

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An attempt is made to assess the significance of rotation in the core-collapse supernova phenomenon, from both observational and theoretical point of view. The data on supernovae particularly indicative of the role of rotation in the collapse-triggered explosion is emphasized. The problem of including the rotation of presupernova core into the supernova theory is considered. A two-dimensional classification scheme of core-collapse supernovae is proposed which unifies “classical” supernovae of type Ib/c and type II, “hypernovae” and some GRB events.

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There is a unique \(\textrm {SU(4)}\otimes \textrm {SU(2)}_{\rm L} \otimes \textrm {SU(2)}_{\rm R}\) gauge model which allows quarks and leptons to be unified at the TeV scale — thereby making the model testable and avoiding the gauge hierarchy problem. In its minimal form, this model could quite naturally accommodate simultaneous solutions to the solar and LSND neutrino oscillation data. The atmospheric neutrino anomaly can be easily accommodated by mirror-symmetrising the minimal model. The model also contains three right-handed neutrinos, with masses in the range 1 keV to \(\sim \) 1 GeV. We investigate the implications of these right-handed neutrinos for early Universe cosmology. It is shown that the minimal model is inconsistent with some of the standard assumptions of the Big Bang model. This motivates an examination of non-standard Big Bang cosmology, such as a low reheating temperature scenario with \(T_{\rm RH} \sim \) MeV. In such a Universe, peaceful co-existence between low-scale quark–lepton gauge unification and early Universe cosmology is possible.