LORENTZ INVARIANT AND SUPERSYMMETRIC INTERPRETATION OF NONCOMMUTATIVE QUANTUM FIELD THEORY

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  • YOSHISHIGE KOBAYASHI
    Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan
  • SHIN SASAKI
    Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan

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<jats:p> In this paper, using a Hopf-algebraic method, we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincaré algebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for [Formula: see text] case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired [Formula: see text] SUSY in [Formula: see text] non(anti)commutative superspace. </jats:p>

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