 0623 R. O. de Mello (1), V. O. Rivelles (2)
 The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
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Jan 25, 06

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Abstract. We prove that the extended Poincare group in (1+1) dimensions is nonnilpotent solvable exponential, and therefore that it belongs to type I. We determine its first and second cohomology groups in order to work out a classification of the twodimensional relativistic elementary systems. Moreover, all irreducible unitary representations of the extended Poincare group are constructed by the orbit method. The most physically interesting class of irreducible representations corresponds to the anomalyfree relativistic particle in (1+1) dimensions, which cannot be fully quantized. However, we show that the corresponding coadjoint orbit of the extended Poincare group determines a covariant maximal polynomial quantization by unbounded operators, which is enough to ensure that the associated quantum dynamical problem can be consistently solved, thus providing a physical interpretation for this particular class of representations.
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