Modification of Newton's law of gravity at very large distances

We discuss a Modified Field Theory (MOFT) in which the number of fields can vary. It is shown that when the number of fields is conserved MOFT reduces to the standard field theory but interaction constants undergo an additional renormalization and acquire a dependence on spatial scales. In particular, the renormalization of the gravitational constant leads to the deviation of the law of gravity from the Newtons law in some range of scales $r_{min} r_{max}$ acquires a new constant value $G^{prime}sim Gr_{max}/r_{min}$. From the dynamical standpoint this looks as if every point source is surrounded with a halo of dark matter. It is also shown that if the maximal scale $r_{max}$ is absent, the homogeneity of the dark matter in the Universe is consistent with a fractal distribution of baryons in space, in which the luminous matter is located on thin two-dimensional surfaces separated by empty regions of ever growing size

Corrections to the Newton and Coulomb potentials caused by effects of spacetime foam

We use an extended quantum field theory (EQFT) hep-th/9911168 to explore possible observational effects of the spacetime. It is shown that as it was expected the spacetime foam can provide quantum bose fields with a cutoff at very small scales, if the energy of zero - point fluctuations of fields is taken into account. It is also shown that EQFT changes the behaviour of massless fields at very large scales (in the classical region). We show that as $rgg 1/mu$ the Coulomb and Newton forces acquire the behaviour $sim 1/r$ (instead of $1/r^{2}$)

Foam-like structure of the Universe

On the quantum stage spacetime had the foam-like structure. When the Universe cools, the foam structure tempers and does not disappear. We show that effects caused by the foamed structure mimic very well the observed Dark Matter phenomena. Moreover, we show that in a foamed space photons undergo a chaotic scattering and together with every discrete source of radiation we should observe a diffuse halo. We show that the distribution of the diffuse halo of radiation around a point-like source repeats exactly the distribution of dark matter around the same source, i.e. the DM halos are sources of the diffuse radiation

On topological bias of discrete sources in the gas of wormholes

The model of space in the form of a static gas of wormholes is considered. It is shown that the scattering on such a gas gives rise to the formation of a specific diffuse halo around every discrete source. Properties of the halo are determined by the distribution of wormholes in space and the halo has to be correlated with the distribution of dark matter. This allows to explain the absence of dark matter in intergalactic gas clouds. Numerical estimates for parameters of the gas of wormholes are also obtained

Corrections to the Newton and Coulomb potentials caused by effects of spacetime foam

We use an extended quantum field theory (EQFT) hep-th/9911168 to explore possible observational effects of the spacetime. It is shown that as it was expected the spacetime foam can provide quantum bose fields with a cutoff at very small scales, if the energy of zero - point fluctuations of fields is taken into account. It is also shown that EQFT changes the behaviour of massless fields at very large scales (in the classical region). We show that as $r\gg 1/\mu$ the Coulomb and Newton forces acquire the behaviour $\sim 1/r$ (instead of $1/r^{2}$).Comment: Latex, 4 page

Ground state and low excitations of an integrable chain with alternating spins

An anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, is investigated \cite{devega}. It is characterized by two real parameters $\bar{c}$ and $\tilde{c}$, the coupling constants of the spin interactions. For the case $\bar{c}<0$ and $\tilde{c}<0$ the ground state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore the low excitations are calculated. It turns out, that apart from free magnon states being the holes in the ground state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to \cite{babelon}. The dispersion law of these excitations is calculated numerically.Comment: 16 pages, LaTeX, uses ioplppt.sty and PicTeX macro

Bilinear identities on Schur symmetric functions

A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.Comment: Accepted to Journal of Nonlinear Mathematical Physics. A reference to a connected result is adde

Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page