This paper has deduced the baryon spectrum using only 2 flavored quarks u and d (each of them has three colored members). From Dirac's sea concept and the quark confinement idea, we conjecture and then assume that the quarks (in the vacuum state) compose colorless particles (uud and udd, hereafter will be called the Lee Particles). Moreover, the Lee Particles lead in a natural way to the construction - a body center cubic lattice in the vacuum. Consequently, there exists a strong interaction periodic field with body center cubic periodic symmetries and an electromagnetic interaction periodic field (from the charged Lee Particles uud) with simple cubic periodic symmetries in the vacuum. In terms of the energy band theory, using a point baryon approximation (i.e., omitting the structure of the Lee Particles), and from the symmetries of the strong interaction periodic field, we have deduced the intrinsic quantum numbers (I, S, C, b, Q) of all baryons and a unified mass formula from which all baryon masses can be found. This theoretical baryon spectrum is in accordance with the experimental results in both intrinsic quantum numbers and masses. These results show that various baryons are the energy band excited states of the Lee Particles. We also predict some new baryons: \Lambda ^0(2559), \Lambda ^0(4279), \Xi_C(3169), \Omega ^-(3619), \Lambda_C^+(6659), \Lambda_b^0(10159) ... Furthermore, from the electromagnetic interaction periodic field of the vacuum material, we predict a super heavy electron spectrum E(166 Gev), E(332 Gev), E(498 Gev) ... We suggest that experiments to find the super heavy electron spectrum and long lifetime baryon \Lambda ^0(2559) should be done.