Time Discretization From Noncommutativity

Understand

We show that a particular noncommutative geometry, sometimes called angular or $\rho$-Minkowski, requires that the spectrum of time be discrete.

• In this noncommutative space the time variable is not commuting with the angular variable in cylindrical coordinates.
• The possible values that the variable can take go from minus infinity to plus infinity, equally spaced by the scale of noncommmutativity.
• Possible self-adjoint extensions of the "time operator" are discussed.