Integrability in string/field theories and Hamiltonian Flows in the Space of Physical Systems

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dc.creatorMironov, A.
dc.date2002-05-20
dc.date.accessioned2026-07-07T04:13:34Z
dc.date.available2026-07-07T04:13:34Z
dc.descriptionIntegrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants or other quantities parameterizing configuration space of physical theories. The dynamics given by variations of coupling constants can be considered as a canonical transformation or, infinitesimally, a Hamiltonian flow in the space of physical systems. We briefly consider here an example of mechanical integrable systems. Then, any function $T(\vec p, \vec q)$ generates a one-parametric family of integrable systems in vicinity of a single system. For integrable system with several coupling constants the corresponding "Hamiltonians" $T_i(\vec p, \vec q)$ satisfy Whitham equations and after quantization (of the original system) become operators satisfying the zero-curvature condition in the space of coupling constants: $$ [\frac{\partial}{\partial g_a} - \hat T_a(\hat{\vec p},\hat{\vec q}),\ \frac{\partial}{\partial g_b} - \hat T_b(\hat{\vec p},\hat{\vec q})] = 0 $$
dc.description15 pages, LaTeX; Proceedings of the workshop "Classical and Quantum Integrable Systems", Protvino, Russia and talk presented at the workshop "Integrable Models, Strings and Quantum Gravity", Chennai, India; January 2002
dc.identifierhttps://arxiv.org/abs/hep-th/0205202
dc.identifierhttp://arxiv.org/abs/hep-th/0205202
dc.identifierTheor.Math.Phys. 135 (2003) 814-827; Teor.Mat.Fiz. 135 (2003) 434-451
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51303
dc.subjectHigh Energy Physics - Theory
dc.titleIntegrability in string/field theories and Hamiltonian Flows in the Space of Physical Systems
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