The scaling properties of the confined phi4 theory

The propagators of the confined fields are obtained in 1/R expansion up to the order (π/R)2, where R is the size of the hadron. The renormalizability of confined phi4 theory in 1 + 3 dimensions is studied. It is multiplicatively renormalizable up to the order (π/R)2 and g sub(R)sup(2), in the minimal subtraction scheme. Besides the usual renormalization constants, the size parameter R is also renormalized. In the renormalization group equation of the n-point function, the anomalous ''size dimension'' is introduced. The inverse of the running size R(t)-1 behaves just like the running mass and it decreases rapidly as the momentum (e sup(t)p) increases. Then the confined theory approaches quickly the unconfined one as t increases. (author)