QCD in the Coulomb gauge II

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QCD in the Coulomb gauge II

• The many body problem
• Gribov-Zwanziger confinement
• Mean-field confinement

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Coulomb gauge Hamiltonian
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Gribov ambiguities
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We will assume Aai(x) are in the F.M.R.
Approximation scheme ? physics input

• Physics
• Helps determining optimal single particle basis
  
• which correlations
  are important

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In QCD
qi ? fabric in 3-space whose (free) excitations
(phonons) have properties
of elementary particles
Weak coupling free quark and gluon, plane wave
basis of single particle states
Strong coupling Constituent quarks and gluons,
solitons, flux tubes, L
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Particle vs. field representation
Particle representation
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Field representation
Harmonic oscillator states ? complete basis !
Make w(k) a variation parameter and use this
basis to diagonalize full H
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A somewhat different approach (A.Szczepaniak,
E.Swanosn, Phys.Rev.D65025012,2002 )
A complete basis ? s.h.o (functional space) wave
function
with w as variational paramters ( there may be
some leackage outside the horizon)
w(k) ¹ k ? a(k) ¹ free qluon operators
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Confinement from the mean field approach
Confinement ? ? gluon self-interactions ? ?
triple-gluon-vertex
Tree
1- loop

Low momentum dominated by ring diagrams
If in the medium (QCD vacuum) w(k)k then a(k)
1/k2 or V(k) 1/k4
/
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Solving the Shrodinger eq. in QCD HYi EYi
Static system
h.o. trial wave fnctional
gluon mass gap eq.
Rainbow-ladder series ? 2 coupled integral
equations
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ladder
rainbow
1)
d(p)
1
p
-1
-

2)
p
w(p)


w(p)
p2/w(p)
3)
f(p)
g


g
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A somewhat different approach (A.Szczepaniak,
E.Swanosn, Phys.Rev.D65025012,2002 )
A complete basis ? s.h.o (functional space) wave
function
with w as variational paramters ( there may be
some leackage outside the horizon)
w(k) ¹ k ? a(k) ¹ free qluon operators