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Equivalent Hamiltonian Systems: New physics at Lagrangian level

Dr. Gilberto Silva Ortigoza

Este seminario se llevará a cabo en la

Sala de Conferencias (111B/302)
Miércoles 29 de febrero de 2012
12:00 hrs.



In this work we use the Hamilton-Jacobi theory to show that locally all the hamiltonian systems with n degrees of freedom are equivalent. That is, there is a canonical transformation connecting two arbitrary hamiltonian systems with the same number of degrees of freedom. This result in particular implies that locally all the hamiltonian systems are equivalent to that of a free particle. We illustrate our result with two particular examples; first we show that the one-dimensional free particle is equivalent to the one-dimensional harmonic oscillator and second that the two-dimensional free particle is equivalent to the two-dimensional Kepler problem.

These simple examples show that the Hamiltonian formulation, via canonical transformations which are not point transformations, allows to introduce new physics at Lagrangian level.