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Solitons, Instantons, and Twistors
TLDR
In this article, the integrability in classical mechanics has been studied in the context of conformal structures and asymmetric reductions in the Lagrangian formalism and field theory, as well as the integration of ASDYM and twistor theory.Abstract:
Preface 1. Integrability in classical mechanics 2. Soliton equations and the Inverse Scattering Transform 3. The hamiltonian formalism and the zero-curvature representation 4. Lie symmetries and reductions 5. The Lagrangian formalism and field theory 6. Gauge field theory 7. Integrability of ASDYM and twistor theory 8. Symmetry reductions and the integrable chiral model 9. Gravitational instantons 10. Anti-self-dual conformal structures Appendix A: Manifolds and Topology Appendix B: Complex analysis Appendix C: Overdetermined PDEs Indexread more
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Scattering Amplitudes and Wilson Loops in Twistor Space
TL;DR: In this paper, Amplitudes and MHV Diagrams are used for on-shell recursion and Wilson Loops are used to identify anomalous events in the MHV diagram. But
Journal ArticleDOI
A simple construction of recursion operators for multidimensional dispersionless integrable systems
TL;DR: In this paper, a simple construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect to the latter is presented.
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On the Relations between Gravity and BF Theories
Laurent Freidel,Simone Speziale +1 more
TL;DR: In this paper, the existing relations between gravity and topological BF theories at the classical level are reviewed, in the light of recent developments, including the Plebanski action in both self-dual and nonchiral formulations, their generalizations, and the MacDowell-Mansouri action.
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Twistor theory at fifty: from contour integrals to twistor strings.
TL;DR: In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold space as mentioned in this paper, and solutions to linear and nonlinear equations of mathematical physics (anti-self-duality equations on Yang-Mills or conformal curvature) can be encoded into twistor cohomology.
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New integrable ( $$3+1$$ 3 + 1 )-dimensional systems and contact geometry
TL;DR: In this article, the authors introduced a systematic construction for integrable (approximately $3+1$$¯¯ )-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields, which are polynomial and rational in the spectral parameter.