On 1 May seminar will be held online only.
Speaker: Konstantin Druzhkov
Title: Internal Lagrangians and gauge systems
Language: English
Zoom Passcode: 0105
Abstract:
In classical mechanics, the Hamiltonian formalism is given in terms of
instantaneous phase spaces of mechanical systems. This explains why it
can be interpreted as an encapsulation of the Lagrangian formalism into
the intrinsic geometry of equations of motion. This observation can be
generalized to the case of arbitrary variational equations. To do this,
we describe instantaneous phase spaces using the intrinsic geometry of
PDEs. The description is given by the lifts of involutive codim-1
distributions from the base of a differential equation viewed as a
bundle with a flat connection (Cartan distribution). Such lifts can be
considered differential equations, which one can regard as gauge
systems. They encode instantaneous phase spaces. In addition, each
Lagrangian of a variational system generates a unique element of a
certain cohomology of the system. We call such elements internal
Lagrangians. Internal Lagrangians can be varied within classes of paths
in the instantaneous phase spaces. This fact yields a direct
(non-covariant) reformulation of the Hamiltonian formalism in terms of
the intrinsic geometry of PDEs. Finally, the non-covariant internal
variational principle gives rise to its covariant child.
The seminar meets on Wednesday evenings at 19:20 MSK in Zoom,
Meeting ID: 88 17 12 1842
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