标题： 二维费米子孤子系统的精确解 显示英文标题

标题： Exact Solutions of a Fermion-Soliton System in Two Dimensions

摘要： 我们研究了一个在(1+1)维中以孤子形式存在的狄拉克粒子和赝标量场的耦合系统，并通过数值方法找到了其中的一些精确解。 我们使用数值方法自洽且非微扰地求解了耦合方程组，得到了费米子的束缚态和孤子的形状。 也就是说，在这个问题中静态孤子的形状不是预设的，而是由方程本身决定的。 这项工作超越了微扰理论，在微扰理论中费米子对孤子的反作用是其一阶修正。 我们将结果与一个可精确求解的模型结果进行比较，在该模型中孤子是预设的。 我们证明，正如预期的那样，我们系统的总能量低于预设的系统。 我们还非微扰地计算了由孤子的存在引起的费米子的真空极化，并展示了结果。 此外，我们计算了孤子质量作为玻色子和费米子质量的函数，并发现结果与Skyrme的唯象假设一致。 最后，我们表明，对于固定参数值，从我们的精确解得到的孤子形状略微依赖于它所耦合的费米子态。 然而，孤子的精确形状始终非常接近孤立的kink。 显示英文摘要

摘要： We investigate a coupled system of a Dirac particle and a pseudoscalar field in the form of a soliton in (1+1) dimensions and find some of its exact solutions numerically. We solve the coupled set of equations self-consistently and non-perturbatively by the use of a numerical method and obtain the bound states of the fermion and the shape of the soliton. That is the shape of the static soliton in this problem is not prescribed and is determined by the equations themselves. This work goes beyond the perturbation theory in which the back reaction of the fermion on soliton is its first order correction. We compare our results to those of an exactly solvable model in which the soliton is prescribed. We show that, as expected, the total energy of our system is lower than the prescribed one. We also compute non-perturbatively the vacuum polarization of the fermion induced by the presence of the soliton and display the results. Moreover, we compute the soliton mass as a function of the boson and fermion masses and find that the results are consistent with Skyrme's phenomenological conjecture. Finally, we show that for fixed values of the parameters, the shape of the soliton obtained from our exact solutions depends slightly on the fermionic state to which it is coupled. However, the exact shape of the soliton is always very close to the isolated kink.