Light-cone behaviour in the relativistic quark oscillator model

Abstract

The light-cone expansion of the commutators of bilocal currents is investigated in the relativistic oscillator quark model proposed by Feynman, Kislinger and Ravndal. An infinite-component field theory formalism describing the oscillator bound states of quarks is introduced in order to define the current operators. The calculation of the lightcone expansions of current commutators shown taht the elastic binding force, aeting between the quarks, does not affect the light-cone behaviour, which remains the same as in the free-quark model. The explicit forms of the deep inelastic structure functionsW1,W2 are also calculated in the free infinite-component field theory model with an arbitrary numberN of oscillating quarks (N=2: mesons,N=3: baryons,N>3: exotics). The scaling limits of the structure functions are sums of δ-function terms coming from the individual quarks even if the instability of excited states is taken into account by giving the trajectory an imaginary part. This indicates that nontrivial scaling functions are possible only in a model which accounts better for strong interactions.