Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces

Abstract

Generators of the super-Poincaré algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the conformal and superconformal symmetry generators in the deformed spaces. This construction is obtained by generalizing the recent work of Wess et al on the Poincaré generators in the $\theta$-deformed Minkowski space, or by using the substitution rules we derived on the basis of the phase-space structures of non-(anti)commutative-space variables. Even with the nonzero deformation parameters the algebras remain unchanged although the comultiplication rules are deformed. The transformation of the fields under deformed symmetry is also discussed. Our construction can be used for systematic developments of field theories in the deformed spaces.

1+19 pages, a typos in the title corrected, to appear in EPJC

References in corpus (3)

• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• Non-Commutative Geometry and Twisted Conformal Symmetry
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces

Cited by in corpus (10)

• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• The three-dimensional non-anticommutative superspace
• Field Theory on Nonanticommutative Superspace
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• D-deformed Wess-Zumino model and its renormalizability properties
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• Twisted SUSY: twisted symmetry versus renormalizability
• Theories on noncommutative spaces and deformed symmetries
• Noncommutative Bundles and Instantons in Tehran