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

  • R. Banerjee
  • C. Lee
  • S. SiwachEmail author
Theoretical Physics


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 θ-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 non-zero 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 development of field theories in the deformed spaces.


Commutation Relation Superconformal Algebra Leibniz Rule Conformal Algebra High Derivative Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.J D Block, Sector IIIS N Bose National Centre for Basic SciencesSalt LakeIndia
  2. 2.School of Physics and Centre for Theoretical PhysicsSeoul National UniversitySeoulKorea

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