THE STRONG COUPLING EXPANSION
47
quite easy to understand what has happened. The Non-Abelian gauge
field describes gluons, having 7=1. When we added a source with
7 = 1 it is energetically favourable for this source to be screened by an
adjacent gluon (this process is shown in the picture (3.55)). If the source
has 7 = 1/2, then in the strong coupling phase such screening is
impossible and we have colour confinement. In principle another phase
is possible in which even 7 = 1/2 will be screened away by 7 = 1 gluons.
For this to happen we must have a cloud containing an infinite number
of gluons. Then statistically they can screen our source. However such a
cloud would have finite energy only if the constituent gluons are
massless. Therefore, we expect that if there is an energy gap in the gauge
theory then the effective cloud will consist of a finite number of gluons
and will be unable to screen half-integer spin. One of the amusing
consequences of this picture is that the string tension between sources
with, say, 7 = 7/2 is the same as for 7 = 1/2 because three units of 7-spin
will be screened by gluons and only 1/2 will remain. All this is a
manifestation of the fact that the electric flux is conserved only mod(l).
The question whether we indeed have a mass gap in the continuum
limit (el 0) cannot be solved by the strong coupling expansion,
because its presence in any order in I/el proves nothing. More subtle
methods are needed. We shall describe some of them in the next
chapter.
47
quite easy to understand what has happened. The Non-Abelian gauge
field describes gluons, having 7=1. When we added a source with
7 = 1 it is energetically favourable for this source to be screened by an
adjacent gluon (this process is shown in the picture (3.55)). If the source
has 7 = 1/2, then in the strong coupling phase such screening is
impossible and we have colour confinement. In principle another phase
is possible in which even 7 = 1/2 will be screened away by 7 = 1 gluons.
For this to happen we must have a cloud containing an infinite number
of gluons. Then statistically they can screen our source. However such a
cloud would have finite energy only if the constituent gluons are
massless. Therefore, we expect that if there is an energy gap in the gauge
theory then the effective cloud will consist of a finite number of gluons
and will be unable to screen half-integer spin. One of the amusing
consequences of this picture is that the string tension between sources
with, say, 7 = 7/2 is the same as for 7 = 1/2 because three units of 7-spin
will be screened by gluons and only 1/2 will remain. All this is a
manifestation of the fact that the electric flux is conserved only mod(l).
The question whether we indeed have a mass gap in the continuum
limit (el 0) cannot be solved by the strong coupling expansion,
because its presence in any order in I/el proves nothing. More subtle
methods are needed. We shall describe some of them in the next
chapter.