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A new Lagrangian dynamic reduction in field theory

François Gay-Balmaz, Tudor S. Ratiu (2010)

Annales de l’institut Fourier

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.

Chaos in D0 brane dynamics

I. Aref'eva, P. Medvedev, O. Rytchkov, I. Volovich (1998)

Banach Center Publications

We consider the classical and quantum dynamics of D0 branes within the Yang-Mills approximation. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed.

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