TL;DR
This paper develops an integrated Lax formalism for the principal chiral model using dual fields, constructs the dual scalar Lagrangian, and analyzes the integrability of the resulting PDE system.
Contribution
It introduces a novel Lax formalism based on dual fields and provides the first dual scalar Lagrangian for the PCM.
Findings
Constructed an explicit Lax formalism using dual fields.
Derived the dual scalar field Lagrangian.
Analyzed the Frobenius integrability of the PDE system.
Abstract
By solving the first-order algebraic field equations which arise in the dual formulation of the D=2 principal chiral model (PCM) we construct an integrated Lax formalism built explicitly on the dual fields of the model rather than the currents. The Lagrangian of the dual scalar field theory is also constructed. Furthermore we present the first-order PDE system for an exponential parametrization of the solutions and discuss the Frobenious integrability of this system.
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