Alan Chodos

Making the massless string massive

We investigate the possibility of associating a finite rest mass density with the relativistic string at the classical level. We choose a modification of the massless Lagrangian which reduces in the non-relativistic limit to the usual non-relativistic string. After studying some simple classical motions of this system, we quantize the massive string in a similar way to the massless case. The Regge trajectories are linear as in the massless case, but their intercepts are shifted downward from unity by an amount proportional to the square of the rest mass density parameter. Our naive quantization procedure is covariant only in 25 space-time dimensions. However, we are able to use the extra degree of freedom implicit in the mass density to modify the Lorentz generators so that covariance is maintained for any dimension less than 25. We envisage hadronic interactions to be introduced through the breaking and joining of strings, as in the massless case, and we discuss the problems associated with the construction of covariant amplitudes when D < 25.

Electromagnetic self-energy of confined massless quarks

Abstract It is suggested that the electromagnetic self-energy of a collection of confined massless quarks may be finite and calculable.

Electromagnetic self-energy of quarks confined to a sphere☆

Abstract We calculate the electromagnetic energy shift, δω, of a massless fermion confined to a sphere. We find δω > 0, in agreement with our previous result for a slab, and in disagreement with the sign needed to obtain the right value of the neutron-proton mass difference in a model in which the hadron consists of confined massless quarks. We consider the effect of a bare mass for the confined quarks, and show that it is then possible for δω to be negative.