Hyperbolic Calculus |
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Authors: | A E Motter M A F Rosa |
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Institution: | (1) Department of Applied Mathematics-IMECC, State University at Carnpinas (UNICAMP), CP 6065, 13081-970 Carnpinas, SP, Brazil |
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Abstract: | The complex numbers are naturally related to rotations and dilatations in the plane. In this paper we present the function
theory associate to the (universal) Clifford algebra forIR
1,0 1], the so called hyperbolic numbers 2,3,4], which can be related to Lorentz transformations and dilatations in the two
dimensional Minkowski space-time. After some brief algebraic interpretations (part 1), we present a “Hyperbolic Calculus”
analogous to the “Calculus of one Complex Variable”. The hyperbolic Cauchy-Riemann conditions, hyperbolic derivatives and
hyperbolic integrals are introduced on parts 2 and 3. Then special emphasis is given in parts 4 and 5 to conformal hyperbolic
transformations which preserve the wave equation, and hyperbolic Riemann surfaces which are naturally associated to classical
string motions. |
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Keywords: | |
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