A solution for the Light Front Tamm-Dancoff equation

相对论束缚态的理解并不好，虽然已经取得了进展。例如，格点规范理论有望成为理解强子作为夸克和胶子的束缚态的有力工具。在格点规范理论的Monte Carlo模拟上的大量工作显示了强相互作用的一些基本性质，然而，关于轻夸克束缚态的精确信息是不可用的。人们一直在寻找格点规范理论的替代工具。光锋Tamm-Dancoff（LFTD）近似方法是作为格点规范理论的替代工具之一而提出的，它是将Tamm-Dancoff近似应用于光锋场理论，而不是通常的等时量子化场论。由于真空在光场框架中是平凡的，因此可以合理地建立一个包含胶子和夸克-反夸克发射的强子的组分夸克模型.本文的目的是在LFTD近似下定量地了解强子的性质，如束缚态能谱、寿命、衰变宽度和波函数.即使在光阵面Tamm-Dancoff近似下，由于自由度太大，不能用解析的方法来处理，我们仅限于时空维数为2的情况，在本研究中我们引入了新的基函数，并利用新的基函数计算了束缚态的质量本征值。我们发现：（1）新的基函数给出了波函数的有效近似;（2）质量本征值与前体的结果一致。

The relativistic bound states are not understood well, although progress has been made. For example, the lattice gauge theory is expected to be a powerful tool for understanding hadrons as the bound states of quarks and gluons. Extensive work on the Monte Carlo simulations of the lattice gauge theory exhibited some basic properties of the strong interaction, however, accurate information on the bound states of the light quarks are not available . Alternative tools to lattice gauge theory has been sought. The light front Tamm-Dancoff(LFTD) approximation method has been proposed as one of the alternative tools to the lattice gauge theory.LFTD is the Tamm-Dancoff approximation applied to light front field theory instead of the usual field theory quantized in the equal time frame. Because the vacuum is trivial in the light front frame, one can legitimately build a constituent quark model of hadrons which includes gluon and quark-antiquark emission.The aim of the present study is to understand quantitatively the properties of the hadrons such as a energy spectrum of a bound state, a life time, a decay width and a wave function by the use of LFTD approximation. Even in the context of Light Front Tamm-Dancoff approximation, the degree of freedom is too many to treat things analytically, we have restricted ourselves in the case where the dimension of the space-time is two.In the present study we have introduced the new basis function and calculated the mass eigenvalue of the bound state using the new basis function. We have found that (1) the new basis function gives an effective approximation of the wavefunction, and (2) the mass eigenvalues are consistent with the results of the precursors.