The band-structure of a one-dimensional, periodic system in a scaling limit: Evans M. Harrell. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 66 KB
• Volume: 119
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(79)90260-4

✦ Synopsis

for which the action is finite and stationary under variations, without assuming any additional boundary conditions at infinity. An element of the proof is the vanishing of the stress tensor for a finite action solution, which actually holds true for the general O(N) o-model. For the two-dimensional O(21 + 1) o-model we exhibit explicit finite action solutions that do not lie in any lower dimensional sphere; the existence of such solutions has been pointed out in the mathematical literature. We also present a rigorous proof, based on Derrick's scaling argument, that there are no nonconstant finite action solutions in more than two dimensions.