Seminar talk, 22 February 2012: Difference between revisions

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{{Talk
{{Talk
| speaker = Maxim Grigoriev
| speaker = Maxim Pavlov
| title = Generating formulations for general gauge theories. Part 2
| title = Reduction of kinetic equations to finite-dimensional systems
| abstract = I recall basic structures and notations of the Batalin-Vilkovisky formalism (and its Hamiltonian analog).  As an illustration, we discuss the standard examples of gauge theories: Yang-Mills, Chern-Simons, gravitation.  We shall also need the AKSZ construction and its relation to free differential algebras, unfolded formalism of higher spin field theory, and the conception of generalized auxiliary fields, and equivalence of gauge theories.  Using the BV formulation in terms of the corresponding jet space we shall introduce the so called generating formulation. The latter exists in two versions: on the level of equations of motion and the Lagrangian level (that is the BV action and odd Poisson bracket). Such a formulation leads to known (and, in number of cases, to unknown) frame like forms of theory (like the Cartan-Weyl gravitation) and closely related to the De Donder–Weyl multisymplectic Hamiltonian formalism.
| abstract = We consider coverings over multidimensional quasi-linear systems of partial differential equations of first order as kinetic equations, for which an approach allowing to derive <math>N</math>-component reductions is known.  The distinction from the approach developed by John Gibbons, Sergey Tsarev and Evgeny Ferapontov and his coauthors in that only one <math>N</math>-component reduction is presented explicitly instead of a whole family parametrized by <math>N</math> function of one argument.  That is, one of solutions of the Gibbons-Tsarev system is automatically presented parametrised by <math>N-1</math> constants.
| slides =
| slides = [[Media:Chesnokov_A.,_Pavlov_M._Reductions_of_kinetic_equations_to_finite_component_systems_(presentation,_2012).pdf|Chesnokov A., Pavlov M. Reductions of kinetic equations to finite component systems (presentation, 2012).pdf]]
| references =  
| references =  
| 79YY-MM-DD = 7987-97-77
| 79YY-MM-DD = 7987-97-77
}}
}}

Latest revision as of 22:59, 19 March 2025

Speaker: Maxim Pavlov

Title: Reduction of kinetic equations to finite-dimensional systems

Abstract:
We consider coverings over multidimensional quasi-linear systems of partial differential equations of first order as kinetic equations, for which an approach allowing to derive -component reductions is known. The distinction from the approach developed by John Gibbons, Sergey Tsarev and Evgeny Ferapontov and his coauthors in that only one -component reduction is presented explicitly instead of a whole family parametrized by function of one argument. That is, one of solutions of the Gibbons-Tsarev system is automatically presented parametrised by constants.

Slides: Chesnokov A., Pavlov M. Reductions of kinetic equations to finite component systems (presentation, 2012).pdf

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