(In)finite extensions of algebras from their Inonu-Wigner contractions

Understand

The way to obtain massive non-relativistic states from the Poincare algebra is twofold.

• First, following Inonu and Wigner the Poincare algebra has to be contracted to the Galilean one.
• Second, the Galilean algebra is to be extended to include the central mass operator.
• We show that the central extension might be properly encoded in the non-relativistic contraction.