Reducing the O(3) model as an effective field theory

Abstract

We consider the O(3) or CP(1) nonlinear sigma model as an effective field theory in a derivative expansion, with the most general Lagrangian that obeys O(3), parity and Lorentz symmetry. We work out the complete list of possible operators (terms) in the Lagrangian and eliminate as many as possible using integrations by parts. We further show at the four-derivative level, that the theory can be shown to avoid the Ostrogradsky instability, because the dependence on the d'Alembertian operator or so-called box, can be eliminated by a field redefinition. Going to the six-derivative order in the derivative expansion, we show that this can no longer be done, unless we are willing to sacrifice Lorentz invariance. By doing so, we can eliminate all dependence on double time derivatives and hence the Ostrogradsky instability or ghost, however, we unveil a remaining dynamical instability that takes the form either as a spiral instability or a runaway instability and estimate the critical field norm, at which the instability sets off.

arXiv commentLaTeX: 40 pages, no figures; V2: comments added and typos corrected

References in corpus (31)

• Modern Theory of Nuclear Forces
• The galileon as a local modification of gravity
• Chiral effective field theory and nuclear forces
• The Standard Model as an Effective Field Theory
• Partially Dual variables in SU(2) Yang-Mills Theory
• Introduction to Effective Field Theory
• The Mesonic Chiral Lagrangian of Order $p^6$
• Multisolitons in a Two-dimensional Skyrme Model
• Are Nonrenormalizable Gauge Theories Renormalizable?
• Healthy degenerate theories with higher derivatives
• Third order equations of motion and the Ostrogradsky instability
• Perturbative unitarity of Lee-Wick quantum field theory
• Quantum Gravity, Fakeons And Microcausality
• Effective Lagrangians with Higher Order Derivatives
• The Theorem of Ostrogradsky
• Supersymmetric Models with Higher Dimensional Operators
• Higher Derivative Field Theories: Degeneracy Conditions and Classes
• Ghost-free theory with third-order time derivatives
• Ghost-free theories with arbitrary higher-order time derivatives
• Higher-derivative operators and effective field theory for general scalar-tensor theories
• The Ostrogradsky instability can be overcome by quantum physics
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• The order $p^8$ mesonic chiral Lagrangian
• Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy
• Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?
• A higher-order Skyrme model
• Fakeons and microcausality: light cones, gravitational waves and the Hubble constant
• Reflection positivity in higher derivative scalar theories
• Asymptotic freedom and higher derivative gauge theories
• Ghostbusters in $f(R)$ supergravity
• Renormalization of gauge theories without cohomology

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• Hilbert series and higher-order Lagrangians for the $O(N)$ model