Automation of Diagrammatic Proofs in Mathematics

Theorems in automated theorem proving are usually proved by logical formal proofs. However, there is a subset of problems which can also be proved in a more informal way by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is more clearly perceived in these than in the corresponding logical proofs: they capture an intuitive notion of truthfulness that humans find easy to see and understand. The proposed research project is to identify and ultimately automate this diagrammatic reasoning on mathematical theorems. The system that we are in the process of implementing will be given a theorem and will (initially) interactively prove it by the use of geometric manipulations on the diagram that the user chooses to be the appropriate ones. These operations will be the inference steps of the proof. The constructive !-rule will be used as a tool to capture the generality of diagrammatic proofs. In this way, we hope to verify and to show that the diagra..

The Standard Model on a D-brane

We present a consistent string theory model which reproduces the Standard Model, consisting of a D3-brane at a simple orbifold singularity. We study some simple features of the phenomenology of the model. We find that the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.Comment: 8 pages Latex, 1 fig. v2: discussion improved, added new reference

Quantum simulation of an extra dimension

We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest non-trivial realization of a fourth dimension corresponds to the creation of a bivolume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.Comment: 5 pages, 3 figures, revtex style;v2 minor changes, references adde

The role of a dynamical measure and dynamical tension in brane creation and growth

The use of a non-Riemannian measure of integration in the action of strings and branes allows the possibility of dynamical tension. In particular, lower dimensional objects living in the string/brane can induce discontinuities in the tension: the effect of pair creation on the string tension is studied. We investigate then the role that these new features can play in string and brane creation and growth. A mechanism is studied by means of which a scalar field can transfer its energy to the tension of strings and branes. An infinite dimensional symmetry group of this theory is discussed. Creation and growth of bubbles in a formulation that requires mass generation for the bulk gauge fields coupled to the branes is also discussed.Comment: LaTeX, 16 pages, 1 figure; Changed the (wrong) orientation of figure 1(a

Multidimensional analogs of geometric s<-->t duality

The usual propetry of st duality for scattering amplitudes, e.g. for Veneziano amplitude, is deeply connected with the 2-dimensional geometry. In particular, a simple geometric construction of such amplitudes was proposed in a joint work by this author and S.Saito (solv-int/9812016). Here we propose analogs of one of those amplitudes associated with multidimensional euclidean spaces, paying most attention to the 3-dimensional case. Our results can be regarded as a variant of "Regge calculus" intimately connected with ideas of the theory of integrable models.Comment: LaTeX2e, pictures using emlines. In this re-submission, an English version of the paper is added (9 pages, file english.tex) to the originally submitted file in Russian (10 pages, russian.tex

Electron plasma oscillations in the near-earth solar wind: Preliminary observations and interpretations

Preliminary results and conclusions of a study of electric field oscillations in the upstream solar wind are reported. The OGO-5 orbits are on the dusk (three) and on the dawn (one) sides of the earth-sun line. It is concluded that there are electron streams produced at or near the bow shock. These streams penetrate the incoming solar wind plasma, and generate quasi-electromagnetic waves. The streams (as inferred from the wave levels) occur without regard to dawn-dusk location, as opposed to the low-frequency MHD upstream disturbances driven by backstreaming protons, which show a definitely strong preference for the dawn-noon sector. The presence of the suprathermal electron streams and associated wave turbulence indicates that some near-earth electron distributions are probably not representative of true solar wind distributions far away from the earth

Comparison of deep space and near-earth observations of plasma turbulence at solar wind discontinuities

Simultaneous observations of plasma waves from the electric field instruments on Pioneer 9 and OGO 5 are used to illustrate the difference between near-earth and deep space conditions. It is shown that the experimental study of true interplanetary wave-particle interactions is difficult to carry out from an earth orbiter because the earth provides significant fluxes of nonthermal particles that generate intense plasma turbulence in the upstream region

The swansong in context: long-timescale X-ray variability of NGC 4051

On 9-11 May 1998, the highly-variable, low luminosity Seyfert 1 galaxy NGC4051 was observed in an unusual low flux state by BeppoSAX (Guainazzi et al. 1998) RXTE and EUVE. We present fits of the 4-15 keV RXTE spectrum and BeppoSAX MECS spectrum obtained during this observation, which are consistent with the interpretation that the source had switched off, leaving only the spectrum of pure reflection from distant cold matter. We place this result in context by showing the X-ray lightcurve of NGC4051 obtained by our RXTE monitoring campaign over the past two and a half years, which shows that the low state lasted for ~150 days before the May observations (implying that the reflecting material is > 10^17 cm from the continuum source) and forms part of a lightcurve showing distinct variations in long-term average flux over timescales > months. We show that the long-timescale component to X-ray variability is intrinsic to the primary continuum and is probably distinct from the variability at shorter timescales, possibly associated with variations in the accretion flow of matter onto the central black hole. As the source approaches the low state, the variability process becomes non-linear. NGC4051 may represent a microcosm of all X-ray variability in radio quiet active galactic nuclei (AGNs), displaying in a few years a variety of flux states and variability properties which more luminous AGNs may pass through on timescales of decades to thousands of years.Comment: 5 pages, accepted for publication in MNRA

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.Comment: 9 pages, no figure

Contact interactions in low scale string models with intersecting D6D6-branes

We evaluate the tree level four fermion string amplitudes in the TeV string mass scale models with intersecting $D6$-branes. The coefficient functions of contact interactions subsuming the contributions of string Regge resonance and winding mode excitations are obtained by subtracting out the contributions from the string massless and massive momentum modes. Numerical applications are developed for the Standard Model like solution of Cremades, Ibanez, and Marchesano for a toroidal orientifold with four intersecting $D6$-brane stacks. The chirality conserving contact interactions of the quarks and leptons are considered in applications to high energy collider and flavor changing neutral current phenomenology. The two main free parameters consist of the string and compactification mass scales, $m_s$ and $M_c$. Useful constraints on these parameters are derived from predictions for the Bhabha scattering differential cross section and for the observables associated to the mass shifts of the neutral meson systems $K-\bar K, B-\bar B, D-\bar D$ and the lepton number violating three-body leptonic decays of the charged leptons $\mu$ and $\tau$.Comment: 34 pages, 7 figure