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1] b(A in Visual Studio .NET
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oa = oalD ] + goal!] + ... etc.
alk ]. If a is assumed to vanish at infinity, so do all the There is no nontrivial solution. However, Eq. (1265) may be regarded as a Schrodinger equation. For a potential A large enough, it can be checked that bound states do exist, i.e., solutions of + il;[a, A;J
with E < 0. Therefore, for intermediate magnitudes of A, there must exist zeroenergy solutions of fast decrease at infinity. This objection seems embarrassing for our program, since the comparison of the quantization in different gauges relies on the assumption of uniqueness of the transformation which relates them. However, since this phenomenon appears for large values of the field, it does not affect the construction of the perturbative series which is by essence a smallfield (smallfluctuation) expansion about a given classical configuration. We shall henceforth discard this Gribov phenomenon. Whenever we talk of uniqueness of the choice of gauge (1264), we understand it in a perturbative sense. The auxiliary conditions (1264) have a nontrivial Poisson bracket with the constraint
NONABELIAN GAUGE FIELDS
{div Aa, rb(y)}XO=YO
OIX~(Y) div A'a(x) OabL\x
= [  + Cabc Vx Ac(X)]03(X y) (1266) We introduce the operator vii: vIIab(x, y) = [ = [  L\xOab
+ Cabc V x Ac(x)J 03(X L\xOab + CabcAc(X) . V xJ 03(X  (1267) where the last expression holds when vii is restricted to the constraint manifold. In the Coulomb gauge, we thus write the generating functional of Green functions as eGc(J) (A)

