In this work, first, we study a flat Friedmann–Robertson–Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann–Robertson–Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the coefficient accompanying the mixed momenta term, two possible cases can be studied: a quintom like case () and a quintessence like case (). For both scenarios classical and quantum solutions are presented.

在这项工作中，首先，我们研究了具有两个标量场但只有一个势项的平坦 Friedmann-Robertson-Walker Universe，可以将其视为一个简单的 quintessence 加上 K-essence 模型。使用哈密顿形式主义，我们能够获得经典和量子解。研究的第二个模型也是具有两个标量场的平坦弗里德曼-罗伯逊-沃克宇宙，区别在于考虑了两个势能以及标准动能和混合项（手性场方法）。关于这第二个模型，表明将伴随混合动量项的系数设置为零，可以研究两种可能的情况：类似quintom 的情况( ) 和类似quintessence 的情况( )。对于这两种情况，都提供了经典和量子解决方案。