New twisted quantum deformations of D= 4 super-Poincare algebra

2011

TheN -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For evenN one can identify the 1DN -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main dierences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.

2012

We present the class of deformations of simple Euclidean superalgebra, which describe the supersymmetrization of some Lie algebraic noncommutativity of D = 4 Euclidean space-time. The presented deformations are generated by the supertwists. We provide new explicit formulae for a chosen twisted D = 4 Euclidean Hopf superalgebra and describe the corresponding quantum covariant deformation of chiral Euclidean superspace.

Symmetries and Groups in Contemporary Physics, 2013

We present the class of deformations of simple Euclidean superalgebra, which describe the supersymmetrization of some Lie algebraic noncommutativity of D = 4 Euclidean space-time. The presented deformations are generated by the supertwists. We provide new explicit formulae for a chosen twisted D = 4 Euclidean Hopf superalgebra and describe the corresponding quantum covariant deformation of chiral Euclidean superspace.

2011

We consider new quantum superspaces, obtained from the superextension of twist deformations of Minkowski spacetime providing Lie-algebraic noncommutativity of spacetime coordinates. The deformed superalgebraic relations describing new quantum superspaces are covariant under the twist-deformed Poincaré supersymmetries. New four classes of supertwist deformations of N = 1 Poincaré superalgebra are investigated and further their Euclidean counterpart presented. Because the proposed supertwists are in odd sector not unitary they are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. Our supertwist deformations in the framework of Hopf-algebraic quantum deformations provide an alternative to the N = 1 2 SUSY Seiberg's star product deformation scheme.

Central European Journal of Physics, 2010

The N -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators.

The European Physical Journal C, 2005

We consider a superextension of the extended Jordanian twist, describing nonstandard quantization of anti-de-Sitter (AdS) superalgebra osp(1|4) in the form of Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of osp(1|4) are given in explicit form. The nonlinear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is to interpret the new super-Jordanian deformation of osp(1|4) superalgebra as deformed D = 4 AdS supersymmetries. Subsequently we perform suitable contraction of quantum Jordanian AdS superalgebra and obtain new κdeformation of D = 4 Poincaré superalgebra, with the bosonic sector describing the light cone κ-deformation of Poincaré symmetries.

Journal of Physics A: Mathematical and General, 1998

The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie superalgebra osp(1|2). The twist element is the same as for the sl(2) Lie algebra due to the embedding of the sl(2) into the superalgebra osp(1|2). The R-matrix has the direct sum structure in the irreducible representations of osp(1|2). The dual quantum group is defined using the FRT-formalism. It includes the Jordanian quantum group SL ξ (2) as subalgebra and Grassmann generators as well.

Journal of High Energy Physics

We present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincaré and Euclidean superalgebras. We consider in detail new family of four supertwists of N = 1 Poincaré superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the N = 1 2 SUSY Seiberg's star product deformation scheme.

Czechoslovak Journal of Physics, 2005

We use the decomposition of o(3, 1) = sl(2; C) 1 ⊕ sl(2; C) 2 in order to describe nonstandard quantum deformation of o(3, 1) linked with Jordanian deformation of sl(2; C). Using twist quantization technique we obtain the deformed coproducts and antipodes which can be expressed in terms of real physical Lorentz generators. We describe the extension of the considered deformation of D = 4 Lorentz algebra to the twist deformation of D = 4 Poincaré algebra with dimensionless deformation parameter.

The European Physical Journal C, 2008

This paper together with the previous one [1] presents the detailed description of all quantum deformations of D = 4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two quantum deformations of the D = 4 Lorentz algebra o(3, 1) obtained by twisting of the standard q-deformation U q (o(3, 1)). For the first twisted q-deformation an Abelian twist depending on Cartan generators of o(3, 1) is used. The second example of twisting provides a quantum deformation of Cremmer-Gervais type for the Lorentz algebra. For completeness we describe also twisting of the Lorentz algebra by standard Jordanian twist. By twist quantization techniques we obtain for these deformations new explicit formulae for the deformed coproducts and antipodes of the o(3, 1)-generators.