On finite action solutions of the nonlinear sigma-model

DOI10.1016/0003-4916(79)90189-1zbMath0412.35089OpenAlexW2080148168MaRDI QIDQ1260302

Simon N. M. Ruijsenaars, Erhard Seiler, Wolf-Dieter Garber, Daniel M. jun. Burns

Publication date: 1979

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0003-4916(79)90189-1

zbMATH Keywords

instantonsvariationsclassical field theoryLagrangeansigma-modelfinite actionDerrick's scaling argument

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Constructive quantum field theory (81T08) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (19)

Liouville theorems for \(F\)-harmonic maps and their applications ⋮ Resurgence and dynamics of \(\mathrm{O}(N)\) and Grassmannian sigma models ⋮ Analyticity of solutions of the O(N) nonlinear \(\sigma\)-model ⋮ Local theory of solutions for the \(0(2k+1)\sigma\)-model ⋮ Harmonic mappings and minimal submanifolds ⋮ Complex and quaternionic analyticity in chiral and gauge theories. I ⋮ How conclusive is the scaling argument? The connection between local and global scale variations of finite action solutions of classical Euler- Lagrange equations ⋮ Nonexistence of proper \(p\)-biharmonic maps and Liouville type theorems. I: Case of \(p\ge 2\) ⋮ Boundary regularity for minima of certain quadratic functionals ⋮ Liouville theorems for Dirac-harmonic maps ⋮ A Liouville theorem for certain nonstationary maps ⋮ ENERGY ESTIMATES AND LIOUVILLE THEOREMS FOR HARMONIC MAPS ⋮ Liouville theorems for harmonic maps ⋮ On vanishing theorems for vector bundle valued \(p\)-forms and their applications ⋮ Nonlinear Dirac equations, monotonicity formulas and Liouville theorems ⋮ Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds ⋮ Regularity Issues for Cosserat Continua and $p$-Harmonic Maps ⋮ A monotonicity formula for Yang-Mills fields ⋮ Some conditions ensuring the vanishing of harmonic differential forms with applications to harmonic maps and Yang-Mills theory

Cites Work

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• Minimal immersions of surfaces in Euclidean spheres
• Polynomial maps from spheres to spheres
• Minimal immersions of spheres into spheres
• On the Volume Decreasing Property of a Class of Real Harmonic Mappings
• Harmonic Mappings of Spheres
• On Minimal Immersions of S 2 Into S 2m
• A Report on Harmonic Maps
• Harmonic Mappings of Riemannian Manifolds

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