How can we construct a covariant model for quarks and partons?
Let us start with a hadron consisting of two quarks bound together by a harmonic oscillator potential. The simplest wave function for this two-particle system is is the harmonic oscillator wave function. Can this wave function be Lorentz-boosted? Its boundary condition can be stated in terms of the spatial coordinates in a given Lorentz frame. Then how about other frames where the spatial and time-like coordinates are mixed? In order to deal with this problem, we need the time-separation variable. Does this variable exist? We are quite familiar with the Bohr radius. It measures the spatial separation between the constituent particles. Then, is there a time-like separation? According to Einstein, the answer is YES. This is the starting point of our plan to construct a harmonic oscillator wave function which can be Lorentz transformed. Let us tackle this problem with the following three figures. The first figure is a space-time diagram of the harmonic oscillator wave function. The second
