%0 Journal Article %J Comm. Math. Phys. 287 (2009) 179-209 %D 2009 %T Gauged Laplacians on quantum Hopf bundles %A Giovanni Landi %A Cesare Reina %A Alessandro Zampini %X We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect. %B Comm. Math. Phys. 287 (2009) 179-209 %I Springer %G en_US %U http://hdl.handle.net/1963/3540 %1 1161 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-24T09:35:24Z\\nNo. of bitstreams: 1\\n0801.3376v2.pdf: 353792 bytes, checksum: 1153ca993428f38ef95f7d31cd727743 (MD5) %R 10.1007/s00220-008-0672-5 %0 Journal Article %J Int. Math. Res. Not. vol. 2008, Article ID rnn038 %D 2008 %T Noncommutative families of instantons %A Giovanni Landi %A Chiara Pagani %A Cesare Reina %A Walter van Suijlekom %X We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$. %B Int. Math. Res. Not. vol. 2008, Article ID rnn038 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3417 %1 918 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:40:47Z\\nNo. of bitstreams: 1\\n0710.0721v2.pdf: 290960 bytes, checksum: 7203f1e1dd34fd90d8d3201c7b813b44 (MD5) %R 10.1093/imrn/rnn038 %0 Journal Article %J Commun. Math. Phys. 263 (2006) 65-88 %D 2006 %T A Hopf bundle over a quantum four-sphere from the symplectic group %A Giovanni Landi %A Chiara Pagani %A Cesare Reina %X We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$. %B Commun. Math. Phys. 263 (2006) 65-88 %G en_US %U http://hdl.handle.net/1963/2179 %1 2065 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T12:11:37Z\\nNo. of bitstreams: 1\\n0407342v2.pdf: 282873 bytes, checksum: e4341c8c3cce9ea132fe6c6916a61526 (MD5) %R 10.1007/s00220-005-1494-3 %0 Journal Article %J J. Phys. A 36 (2003), no. 13, 3829-3840 %D 2003 %T Quantum spin coverings and statistics %A Ludwik Dabrowski %A Cesare Reina %X SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail. %B J. Phys. A 36 (2003), no. 13, 3829-3840 %I IOP Publishing %G en %U http://hdl.handle.net/1963/1667 %1 2451 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:06:10Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1088/0305-4470/36/13/314 %0 Journal Article %J J. Geom. Phys. 37 (2001), no. 1-2, 169-181 %D 2001 %T A note on the super Krichever map %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %X We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa`a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian. %B J. Geom. Phys. 37 (2001), no. 1-2, 169-181 %I SISSA Library %G en %U http://hdl.handle.net/1963/1494 %1 2669 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:11Z (GMT). No. of bitstreams: 1\\nnlin.SI0005062.pdf: 195729 bytes, checksum: daafbab4268655b8f1445ff39762b659 (MD5)\\n Previous issue date: 2000 %R 10.1016/S0393-0440(00)00037-1 %0 Journal Article %J Nucl.Phys. B577 (2000) 547-608 %D 2000 %T 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3 %A Davide Fabbri %A Pietro Fré %A Leonardo Gualtieri %A Cesare Reina %A Alessandro Tomasiello %A Alberto Zaffaroni %A Alessandro Zampa %B Nucl.Phys. B577 (2000) 547-608 %I SISSA Library %G en %U http://hdl.handle.net/1963/1327 %1 3128 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:21Z (GMT). No. of bitstreams: 1\\nhep-th9907219.pdf: 628836 bytes, checksum: c75d99f0a2296bdcc428232f3907ed15 (MD5)\\n Previous issue date: 1999 %R 10.1016/S0550-3213(00)00098-5 %0 Journal Article %J Lett. Math. Phys., 2000, 52, 339 %D 2000 %T A(SLq(2)) at roots of unity is a free module over A(SL(2)) %A Ludwik Dabrowski %A Cesare Reina %A Alessandro Zampa %B Lett. Math. Phys., 2000, 52, 339 %I SISSA Library %G en %U http://hdl.handle.net/1963/1500 %1 2663 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:17Z (GMT). No. of bitstreams: 1\\nmath.QA0004092.pdf: 71107 bytes, checksum: ad69901d378f79db9f98cc05c5caabb4 (MD5)\\n Previous issue date: 2000 %R 10.1023/A:1007601131002 %0 Journal Article %J J. Geom. Phys. 35 (2000), no. 2-3, 239-272 %D 2000 %T Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %B J. Geom. Phys. 35 (2000), no. 2-3, 239-272 %I SISSA Library %G en %U http://hdl.handle.net/1963/1367 %1 3088 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:54Z (GMT). No. of bitstreams: 1\\nnlin.SI0001052.pdf: 330928 bytes, checksum: 88bf53e992f53f4e977dd5329347c85a (MD5)\\n Previous issue date: 1999 %R 10.1016/S0393-0440(00)00007-3 %0 Journal Article %J Phys.Lett. B452 (1999) 244-250 %D 1999 %T Enhanced gauge symmetries on elliptic K3 %A Loriano Bonora %A Cesare Reina %A Alessandro Zampa %X We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s. %B Phys.Lett. B452 (1999) 244-250 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3366 %1 964 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-27T13:09:53Z\\nNo. of bitstreams: 1\\nEnhanced_gauge.pdf: 155859 bytes, checksum: 8dbf403648387d04a1923181897b6ea1 (MD5) %R 10.1016/S0370-2693(99)00295-6 %0 Journal Article %J Lett. Math. Phys. 42 (1997) 349-361 %D 1997 %T Krichever maps, Faà di Bruno polynomials, and cohomology in KP theory %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %X We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning. %B Lett. Math. Phys. 42 (1997) 349-361 %I Springer %G en_US %U http://hdl.handle.net/1963/3539 %1 1162 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T17:16:39Z\\nNo. of bitstreams: 1\\n9704010v1.pdf: 180279 bytes, checksum: c51b95b568001428607e6092a798cce5 (MD5) %R 10.1023/A:1007323118991 %0 Book Section %B Quantization, Coherent States and Poisson Structures, Proc. XIVth Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995, eds. A. Strasburger,\\nS.T. Ali, J.-P. Antoine, J.-P. Gazeau , A. Odzijewicz, Polish Scientific Publisher PWN 1 %D 1995 %T Quantum homogeneous spaces at roots of unity %A Cesare Reina %A Alessandro Zampa %B Quantization, Coherent States and Poisson Structures, Proc. XIVth Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995, eds. A. Strasburger,\\nS.T. Ali, J.-P. Antoine, J.-P. Gazeau , A. Odzijewicz, Polish Scientific Publisher PWN 1 %I SISSA Library %G en %U http://hdl.handle.net/1963/1022 %1 2834 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:41:48Z (GMT). No. of bitstreams: 1\\n120_95.pdf: 543406 bytes, checksum: bfe024146f8ed75ea27cda0399052977 (MD5)\\n Previous issue date: 1995 %0 Journal Article %J Lett. Math. Phys. 29 (1993) 215-217 %D 1993 %T A Borel-Weil-Bott approach to representations of \rm sl\sb q(2,C) %A Davide Franco %A Cesare Reina %X

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.

%B Lett. Math. Phys. 29 (1993) 215-217 %I Springer %G en_US %U http://hdl.handle.net/1963/3538 %1 1163 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T17:04:56Z\\nNo. of bitstreams: 1\\n9305063v1.pdf: 50860 bytes, checksum: 3101cb0bd637adaf2b64c1a8f935b321 (MD5) %R 10.1007/BF00761109 %0 Journal Article %J Phys. Lett. B 297 (1992) 82-88 %D 1992 %T Topological "observables" in semiclassical field theories %A Margherita Nolasco %A Cesare Reina %X

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.

%B Phys. Lett. B 297 (1992) 82-88 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3541 %1 1160 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-24T09:45:37Z\\nNo. of bitstreams: 1\\n9209096v1.pdf: 142343 bytes, checksum: 14465c321b35b3996ff40101c331960b (MD5) %R 10.1016/0370-2693(92)91073-I %0 Journal Article %J J. Math. Phys. 31 (1990), no.4, 948-952 %D 1990 %T N=2 super Riemann surfaces and algebraic geometry %A Cesare Reina %A Gregorio Falqui %X 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. %B J. Math. Phys. 31 (1990), no.4, 948-952 %I American Institute of Physics %G en %U http://hdl.handle.net/1963/807 %1 2984 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:38:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %R 10.1063/1.528775 %0 Journal Article %J Comm.Math.Phys. 31 (1990), no.4, 948 %D 1990 %T A note on the global structure of supermoduli spaces %A Cesare Reina %A Gregorio Falqui %B Comm.Math.Phys. 31 (1990), no.4, 948 %I SISSA Library %G en %U http://hdl.handle.net/1963/806 %1 2985 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:38:11Z (GMT). No. of bitstreams: 1\\n46_89.pdf: 522357 bytes, checksum: 18f63d98e1ce1e711e039894ded5ae7c (MD5)\\n Previous issue date: 1989 %0 Journal Article %D 1988 %T Susy-curves and supermoduli %A Gregorio Falqui %A Cesare Reina %I SISSA Library %G en %U http://hdl.handle.net/1963/761 %1 3030 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:37:15Z (GMT). No. of bitstreams: 1\\n169_88.pdf: 663959 bytes, checksum: 670b0ce089758e0cc68a21d0d2430c0c (MD5)\\n Previous issue date: 1988