abstract

All bialgebra structures on two-dimensional Galilei algebra are classified. The corresponding Lie–Poisson structures on Galilei group are found.

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We integrate analytically the total cross section of the small-angle Bhabha scattering over the complete multiple photon phase space. Some inclusive distributions are also obtained. The differential distributions are taken from the Monte Carlo event generator BHLUMI and correspond to the second-order matrix element with Yennie–Frautschi–Suura (YFS) exponentiation. In the integration we control terms up to leading third-order and sub-leading second-order, in the leading-logarithmic approximation. The analytical results provide a vital cross-check of the correctness of the BHLUMI program. The analytical and Monte Carlo results agree to within \(1.7 \times 10^{-4}\). On the other hand, the calculation gives us unique insight into the relation between exclusive YFS exponentiation and naive inclusive exponentiation.

abstract

In this paper we investigate backreaction of excitations on a planar domain wall in a real scalar field model. The backreaction is investigated in the cases of homogeneous, plane wave and wave packet type excitations. We find that the excited domain wall radiates. The method of calculating backreaction for the general forms of excitations is also presented.

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We show that for the critical dimension \(D_c=2+ \frac {24}{Q}\) of an open parabosonic string, the Fock space is free of negative norms (ghosts).

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Applying the mass shell condition for para-bosonic strings and super strings, new critical space-time dimensions are derived.

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Open parabosonic string BRST transformations are constructed and the critical space-time dimension is derived.

abstract

A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an “action” equal, at the solution, to the one-point function of the puncture operator, and found by solving equations of Gauss–Manin type; (2) For \(A_k\) Landau–Ginzburg models, an extension to large phase space of the usual residue formula for three-point functions is given.

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We present an implementation of the Bose–Einstein effect in a Monte Carlo generator for \(W^-W^+\) production in the \(e^-e^+\) annihilation by means of the weight method. We check that the shift of the \(W\) mass in four jet events due to this effect is similarly small as for the other prescription used recently by Jadach and Zalewski. Possible generalization of this result is shortly discussed.

abstract

In this short note a simple quantum chemical type of approach to electron correlations in \(d\)-dimensional Hubbard model is proposed. In essence, the method is very closely related to CEPA-0 approximation (also to Gutzwiller approximation and to the Local ansatz) and as such is no novelty. The real aim is to provide unsophisticated and computationally cheap method which allows for an easy treatment of electron correlations in finite cluster models with a simple Hubbard type Hamiltonians.

abstract

A simple and realistic model of bistable chemical system in which running fronts can be observed is studied. Mesoscopic characteristics of the model are obtained by numerical simulations of the master equation for spatially distributed system. Velocity of the front and its width obtained in the simulations agree well with the phenomenological description. However, for small diffusion coefficient fluctuations grow locally to a macroscopic size and create pulses. Such effects cannot be described by the phenomenological approach.