Villarceau foliated solitons in the two-dimensional O(3) nonlinear sigma model
نویسندگان
چکیده
We obtain the complete space of solutions, in the two-dimensional O(3) nonlinear sigma model, which are foliated by Villarceau circles. In particular, we prove the existence of solitons that admit a foliation by nonparallel circles. This contrasts with the Plateau context, where solitons foliated by nonparallel circles cannot exist. These solitons carry topological charges that are holographically computed via the Gauss–Bonnet formula. c © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Knot Solitons
The existence of ring-like and knotted solitons in O(3) non-linear σ model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen. †[email protected]; [email protected] †† permanent address Introduction: Recently the possible existence of knotlike solitons in nonlinear field theories has been argued[1, 2]. ...
متن کاملA geometric algorithm to construct new solitons in the O(3) nonlinear sigma model
The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...
متن کاملN ov 2 00 2 A Geometric Algorithm to construct new solitons in the O ( 3 ) Nonlinear Sigma Model Manuel
The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...
متن کاملBARRIER PENETRATION IN 1 + 1 - DIMENSIONAL O ( n ) SIGMA MODELS
The O(n) nonlinear sigma model in 1 + 1 dimensions is examined as quantum mechanics on an infinite-dimensional configuration space. Two metrics are defined in this space. One of these metrics is the same as Feynman's distance, but we show his conclusions concerning potential energy versus distance from the classical vacuum are incorrect. The potential-energy functional is found to have barriers...
متن کاملTopological and Nontopological Solitons in a Gauged O(3) Sigma Model with Chern-Simons term
TheO(3) nonlinear sigma model with its U(1) subgroup gauged, where the gauge field dynamics is solely governed by a Chern-Simons term, admits both topological as well as nontopological self-dual soliton solutions for a specific choice of the potential. It turns out that the topological solitons are infinitely degenerate in any given sector. ∗ E-mail: [email protected] ∗∗ E-mail: sanjay@iopb....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006