Spin Networks and Quantum Gravity

We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a generalization of Penrose's spin netoworks. The new basis fully reduces the spinor identities (SU(2) Mandelstam identities) and simplifies calculations in non-perturbative quantum gravity. In particular, it allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation. Since the states in this basis diagnolize operators that represent the three geometry of space, such as the area and volumes of arbitrary surfaces and regions, these states provide a discrete picture of quantum geometry at the Planck scale.Comment: 42 page

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

Beauty photoproduction measured using decays into muons in dijet events in ep collisions at s\sqrt{s}=318 GeV

The photoproduction of beauty quarks in events with two jets and a muon has been measured with the ZEUS detector at HERA using an integrated luminosity of 110 pb$^{- 1}$. The fraction of jets containing b quarks was extracted from the transverse momentum distribution of the muon relative to the closest jet. Differential cross sections for beauty production as a function of the transverse momentum and pseudorapidity of the muon, of the associated jet and of $x_{\gamma}^{jets}$, the fraction of the photon's momentum participating in the hard process, are compared with MC models and QCD predictions made at next-to-leading order. The latter give a good description of the data.Comment: 32 pages, 6 tables, 7 figures Table 6 and Figure 7 revised September 200

κ - Deformed Poincaré Algebra and Some Physical Consequences

The κ-deformed D = 4 Poincaré algebra is obtained by a special contraction of the real quantum Lie algebra Uq(0(3, 2)). We describe this contraction and study the consequences of the κ-deformation of the relativistic energy formula for the kinematics of scalar massless and massive particules. The notion of κ-relativistic energy region is defined. The κ-deformed quantized Klein-Gordon scalar field is introduced

Measurement of the diffractive cross-section in deep inelastic scattering

Diffractive scattering of $\gamma^* p \to X + N$, where $N$ is either a proton or a nucleonic system with $M_N~<~4$~GeV has been measured in deep inelastic scattering (DIS) at HERA. The cross section was determined by a novel method as a function of the $\gamma^* p$ c.m. energy $W$ between 60 and 245~GeV and of the mass $M_X$ of the system $X$ up to 15~GeV at average $Q^2$ values of 14 and 31~GeV$^2$. The diffractive cross section $d\sigma^{diff} /dM_X$ is, within errors, found to rise linearly with $W$. Parameterizing the $W$ dependence by the form d\sigma^{diff}/dM_X \propto (W^2)^{(2\overline{\mbox{\alpha_{_{I\hspace{-0.2em}P}}}} -2)} the DIS data yield for the pomeron trajectory \overline{\mbox{\alpha_{_{I\hspace{-0.2em}P}}}} = 1.23 \pm 0.02(stat) \pm 0.04 (syst) averaged over $t$ in the measured kinematic range assuming the longitudinal photon contribution to be zero. This value for the pomeron trajectory is substantially larger than \overline{\mbox{\alpha_{_{I\hspace{-0.2em}P}}}} extracted from soft interactions. The value of \overline{\mbox{\alpha_{_{I\hspace{-0.2em}P}}}} measured in this analysis suggests that a substantial part of the diffractive DIS cross section originates from processes which can be described by perturbative QCD. From the measured diffractive cross sections the diffractive structure function of the proton F^{D(3)}_2(\beta,Q^2, \mbox{x_{_{I\hspace{-0.2em}P}}}) has been determined, where $\beta$ is the momentum fraction of the struck quark in the pomeron. The form F^{D(3)}_2 = constant \cdot (1/ \mbox{x_{_{I\hspace{-0.2em}P}}})^a gives a good fit to the data in all $\beta$ and $Q^2$ intervals with $a = 1.46 \pm 0.04 (stat) \pmComment: 45 pages, including 16 figure