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Fioresi, R., Latini, E., Lledo, M. A., & Nadal, F. A. (2018). The Segre embedding of the quantum conformal superspace. Adv. Theor. Math. Phys., 22(8), 1939–2000.
Abstract: In this paper we study the quantum deformation of the superflag Fl(2 vertical bar 0, 2 vertical bar 1, 4 vertical bar 1), and its big cell, describing the complex conformal and Minkowski superspaces respectively. In particular, we realize their projective embedding via a generalization to the super world of the Segre map and we use it to construct a quantum deformation of the super line bundle realizing this embedding. This strategy allows us to obtain a description of the quantum coordinate superring of the superflag that is then naturally equipped with a coaction of the quantum complex conformal supergroup SLq (4 vertical bar 1).
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Lledo, M. A., & Sommovigo, L. (2010). Torsion formulation of gravity. Class. Quantum Gravity, 27(6), 065014–16pp.
Abstract: We explain precisely what it means to have a connection with torsion as a solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.
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Cervantes, D., Fioresi, R., Lledo, M. A., & Nadal, F. A. (2012). Quadratic deformation of Minkowski space. Fortschritte Phys.-Prog. Phys., 60(9-10), 970–976.
Abstract: We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.
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Fioresi, R., Lledo, M. A., & Razzaq, J. (2022). N=2 quantum chiral superfields and quantum super bundles. J. Phys. A, 55(38), 384012–19pp.
Abstract: We give the superalgebra of N = 2 chiral (and antichiral) quantum superfields realized as a subalgebra of the quantum supergroup SL q (4|2). The multiplication law in the quantum supergroup induces a coaction on the set of chiral superfields. We also realize the quantum deformation of the chiral Minkowski superspace as a quantum principal bundle.
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Cervantes, D., Fioresi, R., Lledo, M. A., & Nadal, F. A. (2016). Quantum Twistors. P-Adic Num., 8(1), 2–30.
Abstract: We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.
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