The Construction Of The Baryon Wave Function

Baryon is composed of three quarks, it is a important topic to study the structure of baryon in elementary particle physics. How to construct the flavor wave function of baryon is the key to study the multiquark states. In this work, we use a new method, which was proposed recently, to construct flavor wave function. This new method is that we use the outer product rule and the Gelfand basis and the isoscalar factor (ISF) which is obtained from the reduction of Un(?)Un-1, to construct baryon flavor wave functions.Firstly, the SU(2) flavor wave functions are given including the u and d quarks. Then, using the same method, the SU(3) flavor wave functions are constructed by including the u, dand s quarks. Compared with other works, we find our results are completely consistent with those from other works. Further the SU(4) flavor wave are constructed by including the u, d, s and c quarks. On the basis of SU(4), we extend into the SU(5) flavor wave func-tions by further introducing the b quark. Finally, some applications are discussed, such as constructing spin wave function, and also the color wave function, and how to calculate the matrix elements for some flavor operators used in hadron physics.In summary, we show that the new method used in this work can be easily extended to many body system, and also easily be extended to spin space, color space and other space. It may be very helpful to further study the structure of many body systems.