Study on Deformed Galilean Symmetries in Noncommutative Phase Space

The deformed Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under deformed phase space transformations is constructed. The Dirac brackets of this model reproduce the original non-commutative algebra. Also, the deformed generators are abstracted from this model in a consistent manner. Finally, the role of Jacobi identities is emphasised to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.