Abstract: By the means of the semi-classical approximation, the density of quantum states for relativistic particles in n-dimensional space is derived and thus the lower dimensional results are obtained, and then apply it in the research of the black body radiation of n- dimensional space, the universal expressions of two kinds of particles in black body radiation is inferred, our main formulas which is yielded in the lower dimensions are consistent with our expected results for the three-dimensional space, which plays an important role for deepening the teaching and research in the lower dimensions.

Key words: any dimensions, relativistic particles, density of quantum states, black body radiation