Introduction to QCD slides - P.Hoyer.pdf - High Energy Physics Group

Matter field:
Paul Hoyer Mugla 2010
ψ(x) → U(x)ψ(x)
Physical Review 96 (1954) 191
For a local gauge transformation defined by an SU(2) matrix U(x), Yang and
Mills found that the theory is symmetric provided the fields transform as:
Gauge field: Aµ(x) → U(x)Aµ(x)U † (x) − i
g U(x)∂µU † (x)
The same rule holds for any group, such as SU(3). In QED,
g is the same
for all ψ!
U(x) =e ieΛ(x) Then U1U2 = U2U1, i.e., all group elements commute,
hence the U(1) gauge symmetry is said to be abelian.
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