Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-11-21
Eur.Phys.J.C48:305-313,2006
Physics
High Energy Physics
High Energy Physics - Theory
1+19 pages, a typos in the title corrected, to appear in EPJC
Scientific paper
10.1140/epjc/s10052-006-0005-9
Generators of the super-Poincar\'e 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 Poincar\'e 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.
Banerjee Rabin
Lee Choonkyu
Siwach Sanjay
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