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|Paper IPM / Physic / 8489||
In this paper we consider the massive and massless action for relativistic particle in D-dimensional flat space�time.
We show that the Poincare� space�time algebra in the commutator version, and the Killing field provides the generators
of the Poincare� algebra. We apply the non-commutative version to action, which is not Poincare� invariant. This leads us
to consider the twisted Poincare� transformation, finally by using this transformation, we see that the action is invariant.
By using the non-commutative space in massless action, in contrast to the commutative case the scale and conformal invariance
is broken by massive term [For an interesting discussion of the cosmological constant problem see A. Zee,
Dark energy and the nature of the graviton, <arXiv:hep-th/0309032>].
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