Phase transitions for one (and zero)—Dimensional systems with short-range forces: Roger Balian. Service de Physique Théorique, Centre d'Études Nucléaires de Saclay, BP no 2, 91190 Gif-sur-Yvette, France and Gérard Toulouse. Laboratoire de Physique des Solides, Laboratoire associé au CNRS, Université Paris-Sud, Centre d'Orsay, 91404 Orsay, France

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 86 KB
• Volume: 81
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(73)90173-5

✦ Synopsis

This article is a theoretical investigation of generalized Noether's theorem, which, though unconcerned with considerations such as coordinate transformations, symmetry, and invariance, is the basic mechanism of conventional Noether's theorem, its extensions, and its inverse. The generalized theorem is a completely new approach to the subject-formally, conceptually, and practically. It is an association, for a set of field equations, of field variations with conserved currents. The theorem is stated from two points of view and analyzed with regard to its interpretation and its formal and conceptual relation to conventional Noether's theorem and extensions, transformation groups, and Hamilton's principle. The inverse theorem is also treated. The role of coordinate transformations in conventional Noether's theorem is analyzed.