Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures

• Null compactification techniques are used to derive the nonrelativistic gauged Schrödinger equation.
• Compactification of both Klein–Gordon and Maxwell theories are revisited.
• Connections with Kaluza–Klein-like Bargmann frameworks are established.

The Schrödinger equation for a spinless particle in presence of an external electromagnetic field is derived by means of null compactification of five dimensional massless Klein–Gordon theory and five–dimensional Maxwell electrodynamics. Connections with Kaluza–Klein-like Bargmann frameworks are established.