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The field equations of elementary domains proposed by Yukawa in 1968 arestudied from the viewpoint of particle embedded $\mbox{AdS}_5$ spacetime withwarp factor. The fifth dimension in $\mbox{AdS}_5$ is known to produce thebranes associated with the energy hierarchy as a effect of the warp factor. Theparticles embedded in this spacetime behave as those in an infinite square wellpotential due to the boundary conditions in the fifth dimension. Then thesuperposition of the fields for those particles leads to a Yukawa's domain typeof difference equation under some conditions. As a new perspective on AdSspacetime, we investigate the mechanisms that lie between the domain type offield equations in this sense and the spacetime with a compact extra dimensionin detail.

An Approach to Yukawa's Elementary Domain Based on $\mbox{AdS}_5$ Spacetime