München 1997 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 6: Klassische Feldtheorie und Quantisierung

MP 6.5: Fachvortrag

Mittwoch, 19. März 1997, 17:20–17:40, HS 117

Reducing the algebraic complexity of Carathéodory’s canonical formulation for fields by H"older-type transformations — •Wulf B"ottger¹ and H.A. Kastrup² — ¹Institut f"ur Theoretische Physik E, RWTH Aachen — ²Institut f"ut Theoretische Physik E, RWTH Aachen

Carathéodory’s Hamilton-Jacobi theory is the only manifest covariant formulation for fields that preserves the dimension of the wave fronts as well as their transversality to the extremals known from mechanics.

However, the price for this appealing geometrical property is a complex algebraic structure of the canonical framework which is much more sophisticated than that of DeDonder and Weyl.

It will be shown that employing a coordinate transformation resembling a sequence of two H"older transformations simplifies the structure of Carathéodory’s Hamilton-Jacobi equation and the associated integrability conditions considerably. Applying this procedure to a bosonic string theory yields a large class of nonlinear PDEs.