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 p
r
. 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 m
s
/m
c
≊m
b
/m
t
≊m
b
’
/m
b
’
holds independently of the parameters in the potential. Differences and similarities between quantum rings and Nambu strings are discussed.