El Cuerpo
Académico de Partículas Campos y Relatividad General invita
cordialmente a su próximo seminario
Equivalent
Hamiltonian Systems: New physics at Lagrangian level
Dr. Gilberto
Silva Ortigoza
FCFM - BUAP
Este
seminario se llevará a cabo en la
Sala de Conferencias (111B/302)
Miércoles 29 de febrero de 2012
12:00 hrs.
Resumen:
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.