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            <title xml:lang="en">Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality</title>
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                <title xml:lang="en">Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality</title>
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              <p>Multicomplex numbers of order n have an associated trigonometry (multisine functions with (n-1) parameters) leading to a natural extension of the sine-Gordon model. The parameters are constrained from the requirement of local current conservation. In two dimensions for n &lt; 6 known integrable models (deformed Toda and non-linear sigma, pure affine Toda...) with dual counterparts are obtained in this way from the multicomplex space MC itself and from the natural embedding $\\MC_n \\subset \\MMC_m, n &lt; m$. For $ n \\ge 6$ a generic constraint on the space of parametersis obtained from current conservation at first order in the interaction Lagragien.</p>
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