Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schr\"odinger equation

The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h_6 and its associated quantum universal R-matrix. A deformed one-boson representation for this algebra is deduced and applied to construct a first order deformation of the differential equation that generates the two-photon algebra eigenstates in Quantum Optics. On the other hand, the isomorphism between h_6 and the (1+1) Schr\"odinger algebra leads to a new quantum deformation for the latter for which a differential-difference realization is presented. From it, a time discretization of the heat-Schr\"odinger equation is obtained and the quantum Schr\"odinger generators are shown to be symmetry operators.Comment: 12 pages, LaTe

Small Angle Polarization in High Energy P--P Scattering Through Nonperturbative Chiral Symmetry Breaking

We show that a large anomalous contribution due to nonperturbative instanton-like gluonic field configurations to the axial charge of the proton implies high-energy spin effects in $p-p$ elastic scattering. This is the same mechanism which is responsible for anomalous baryon number violation at high energy in the standard model. We compute the proton polarization due to these effects and we show that it is proportional to the center-of-mass scattering angle with a universal (energy-independent) slope of order unity.Comment: (13 pages, 2 figures

Diffractive Photoproduction of Jets with a Direct Pomeron Coupling at HERA

We investigate in detail the effect of a direct pomeron coupling to quarks on the production of jets in $ep$ scattering with almost real photons. Jet production via a direct pomeron coupling is compared with the resolved--pomeron mechanism. We consider both direct and resolved photoproduction. Rapidity and transverse momentum distributions are calculated and compared with preliminary H1 and ZEUS data.Comment: 21 pages, Latex file, 7 figures (uuencoded) enclosed, Preprint DESY 94-140, KEK-TH-407 and KEK Preprint 94-7