Seminar talk, 29 February 2012

From Geometry of Differential Equations
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Speaker: Maxim Grigoriev

Title: Generating formulations for general gauge theories. Part 2

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.