Yael Medina Quiróz

The use of symmetry methods to solve a system of differential equations (ordinary and/or partial). These symmetry methods are then applied to the equations of motion of different physical systems, in particular to those that rise from the formalism of deformation quantization. A comparison of their corresponding Lie group (local) is then made between this formalism and its classical counterpart. It is important to make a distinction between the “physical” group and the “mathematical” group of the system of differential equations. The “mathematical” group are those transformations that leave the system of differential equations invariant, while the “physical” group are those transformations that leave the functional action of the system invariant. Once its Lie group (local) is computed one can study non-trivial conservation laws, transform solutions of the system of differential equations to other solutions, make a classification of families of differential equations, etc.