absurdum argument. If g is small, we can approximate the beta function at these energies by a Taylor series expansion: where ¯ g is the deviation of g from its value at p = M . We define the value of g at p = M as g$_{R}$ : g$_{R}$ ≡ g ( p = M ). Any perturbative deviation from g$_{R}$ will involve some sort of interaction. With each interaction, at least one power of the coupling constant will enter. Hence we can set A = 0. B, C, D . . . can be calculated quantitatively ‡ ; the method is detailed in [14]. Here we are only concerned with the qualitative effects of the the leading coefficient of (1.9). The first non-zero contribution to (1.9) is canon- ically called β$_{1}$ . There are three possibilities: For β$_{1}$ ( g ) > 0, the coupling constant becomes small in the infrared region of the theory. This is the case with QED, and allows us to successfully use perturbation theory at every-day energies. However, in the high energy, ultraviolet regime, the coupling constant gets larger and larger, eventually reaching the point where perturbation theory is no longer valid. Fortunately, in QED, the energy level where this occurs is much much higher than any reachable today. Furthermore, new physics is expected to appear a long time before we reach such energies. $^{‡}$In QCD with 6 flavours of quark, B = C = 0 and D = − 7 16 π 2 [14] 9 β ( g ) = A + B ¯ g + C ¯ g 2 + D ¯ g $^{3}$. . . (1.9) 1. β$_{1}$ > 0 2. β$_{1}$ = 0 3. β$_{1}$ < 0