Arbitrary spin Galilean oscillator

• Dirac oscillator generalized to include spin.
• Galilean relativity is the essential tool for this extension.
• For general spin zero point energy is eliminated and a spin–orbit coupling found which is proportional to 1/S1/S.
• Nonminimal theories are shown to allow varying spin–orbit coupling.

The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin–orbit coupling term. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin–orbit term has a 1/S1/S behavior.