An algebraic model is proposed which simulates the strong interaction between quarks, for the description of hadron states. The model is based on the SO(4)-group. The effects of the long-range quark–quark interactions, like zero-color confined states, symmetries and energy dependence, required for a correct description of hadrons at low energy, are considered through the assignment of SO(4)-quantum numbers to the hadron states. A simpler version of this model was used earlier to illustrate the relevance of many-body methods implemented for pseudo-scalar and vector meson-like states, particularly the low energy portion of the pion spectrum. In this work an algebraic Hamiltonian is proposed, its spectrum is calculated for several meson quantum numbers J ^P = 0, 1, 2, as well as baryon quantum numbers , and compared to data. Our purpose is to investigate how adequate is this model when applied to the description of several characteristics of the hadron spectrum, like the observed masses, density of states and sequences of spin and parity.

提出了一种模拟夸克之间强相互作用的代数模型，用于描述强子态。该模型基于SO (4)-组。通过将SO (4)-量子数分配给强子态。这个模型的一个更简单的版本早先被用来说明为伪标量和矢量介子状态实现的多体方法的相关性，特别是 pion 光谱的低能量部分。在这项工作中提出了一个代数哈密顿量，它的频谱是为几个介子量子数计算的J ^P = 0, 1, 2，以及重子量子数，并与数据进行比较。我们的目的是研究当应用于描述强子光谱的几个特征时，这个模型有多充分，比如观察到的质量、状态密度以及自旋和奇偶校验序列。