Quantum equations for simple interacting strings: Their exact solutions and physical implications

Abstract

A string can have a simple potential interaction only when it has a constant radius. The Hamiltonian for such a string is characterized by a cyclic radial momentum pr. Physical properties of this interacting string (or ‘‘ring’’) are illustrated by exact solutions of quantum ring equations (with a ‘‘flavor potential’’) in the four-dimensional space-time and in a particular reference frame. The energy eigenstates of the ring are ultrastable because flavor transitions between different states are forbidden. Furthermore, the ring can be permanently confined by a potential ∝r−1 ln(λr), and the size of the ring can be detected by scattering processes. In the absence of the electroweak interaction, a simple composite quark model based on a particle–ring interaction is discussed. It is found that the relation ms/mc≊mb/mt≊mb′/mb′ holds independently of the parameters in the potential. Differences and similarities between quantum rings and Nambu strings are discussed.