Finite dimesional Hamiltonian formalism for gauge and field theories

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized Poisson $\mathfrak{p}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field.Comment: 52 pages. In this paper we give a more general hamiltonian formulation for a gauge and field theories, it's an extension of our previous paper math-ph/000402

Foundations of mathematics and physics one century after Hilbert: new perspectives

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too

Gravitation multisymplectique

Ce travail de thèse s'inscrit dans cadre de l'application de la Géométrie Différentielle pour la Relativité Générale, en particulier elle présente l'approche de la Géométrie Multisymplectique pour la formulation de plusieurs exemple de théorie de jauge, et de la théorie de gravitation. La Géométrie Multisymplectique nous offre un cadre géométrique pour formuler la théorie classique des champs de manière indépendante des coordonnées, sur des espace-temps généraux. L'idée clé est de construire une description Hamiltonienne de la théorie des champs compatible avec les Principes de la relativité restreinte et générale, des théories des cordes et plus généralement avec toute tentative de comprendre la gravitation. Lespace-temps émerge de la dynamique elle-même et il n'y a pas de séparation espace-temps/champs donnée a priori. n'y a pas de structure d'espace-temps donnée a priori. Les coordonnées d'espace-temps émergent de l'analyse des quantités observables et de la dynamique.PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF

Cartan's soldered spaces and conservation laws in physics

International audienc