A solution for the Light Front Tamm-Dancoff equation

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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.