We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

PB - Springer UR - http://hdl.handle.net/1963/3538 U1 - 1163 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological "observables" in semiclassical field theories JF - Phys. Lett. B 297 (1992) 82-88 Y1 - 1992 A1 - Margherita Nolasco A1 - Cesare Reina AB -We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

PB - Elsevier UR - http://hdl.handle.net/1963/3541 U1 - 1160 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - N=2 super Riemann surfaces and algebraic geometry JF - J. Math. Phys. 31 (1990), no.4, 948-952 Y1 - 1990 A1 - Cesare Reina A1 - Gregorio Falqui AB - The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems. PB - American Institute of Physics UR - http://hdl.handle.net/1963/807 U1 - 2984 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A note on the global structure of supermoduli spaces JF - Comm.Math.Phys. 31 (1990), no.4, 948 Y1 - 1990 A1 - Cesare Reina A1 - Gregorio Falqui PB - SISSA Library UR - http://hdl.handle.net/1963/806 U1 - 2985 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Susy-curves and supermoduli Y1 - 1988 A1 - Gregorio Falqui A1 - Cesare Reina PB - SISSA Library UR - http://hdl.handle.net/1963/761 U1 - 3030 U2 - Mathematics U3 - Mathematical Physics ER -