we need to formulate the A = 1 super-symmetric Gauge theory in D-dimensions. The
Lagrangian density we start off with is given by
L = TrFFl' + iTrF0F(,,' ig [A,, ]) (2-7)
Fl = ,A A ,A, ig [A, A,], (2-8)
where FP are the D dimensional Dirac gamma matrices. Lightcone gauge dictates A_ = 0
and A+ is eliminated using Gauss' law. The "time" evolution operator P- is obtained in
order to read off the Lightcone Feynman rules:
P- dxdx- (T + C +Q) (2-9)
where the individual terms which give the various vertices of the Feynman rules are given
by the expressions below. Using the Lightcone Dirac equation and Gauss' law in the
A_ = 0 Gauge one arrives at
T TrOAjAj i Tr bt a-
C = igTrOAk A A Ak A A Ak + Tr )cb [ Ak ']
g + k Ok }b
-!Tr{ [ctAl(k nk)cb b b V. A, b)
Q = Tr 2-[Ak, OAk + AAj[Ai,Aj] + + Tr {,-', t} b bt (210)
-ig2 Tr -( [_Ak, Ak]{ t}) + Tr{ [CA](fk + )nkcb [Ak ,,
where
X Y = X Y X Y. (2-11)
Although we do intend to refer the reader to the original work [7, 16] for the details of the
dimensional reduction and formulation of the individual vertices of the theory, we present
this expression for the Lightcone Gauge Hamiltonian in order for the reader to be able
to read off the Feynman rules and vertex factors. In the next section we indicate (albeit