A pair of 2D harmonic oscillators at a point and Dirac eq.

[Spinnor]

A two-dimensional harmonic oscillator is associated with the group Su(2). What is that association?

Solutions to the Dirac equation require a pair of spinors at each point?

Can we think think of spacetime as having pairs of 2D harmonic oscillators at each point?

Thanks for any help.

 

[Spinnor]

A two-dimensional harmonic oscillator is associated with the group Su(2). What is that association?

Solutions to the Dirac equation require a pair of spinors at each point?

Can we think think of spacetime as having pairs of 2D harmonic oscillators at each point?

Thanks for any help.

Obviously the oscillators would be coupled to their neighbors with insight from the Dirac equation.