1. in SU(N) Gauge Field Theory
The Non-Perturbative Self-Consistent Model
in SU(N) Gauge Field Theory
A.V.KOSHELKIN
Moscow Institute for Physics and Engineering
HCP'11, November 2011, Paris, France

2. 1.Statement of Problem and Main Goal
HCP'11, November 2011, Paris, France

3. HCP'11, 14-18 November 2011, Paris, France
2.Key Approximations
3.The main goals are
1) to obtained such solutions that both the Yang-Mills and Dirac Equation
would be satisfied together;
2) to quantize the fields;
3) to apply the obtained results to QCD .
HCP'11, November 2011, Paris, France

4. HCP'11, 14-18 November 2011, Paris, France
4.RESULTS OF SOLUTIONS
i) The Yang-Mills equation
ANSATZ
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5. HCP'11, 14-18 November 2011, Paris, France
ii) The Dirac equation
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6. HCP'11, 14-18 November 2011, Paris, France

7. 5. Self-Consistent Solution
a) Gauge field
b) Fermion field
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8. HCP'11, 14-18 November 2011, Paris, France
c) Relation equations
The problem is solvable when the dimension of the gauge group In this way, the currents generated by fermions and gauge field exactly compensate each other.
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9. HCP'11, 14-18 November 2011, Paris, France
Quantizing the Yang-Mills field
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10. 6. Fermion and Gauge Field in Developed Model
In terms of the multi particle problem,
the solutions correspond to individual states of particles
the solutions correspond to collective states (Fermi liquid-like)
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11. Fermion effective mass.
EQUILIBRIUM 1) 2)
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12. HCP'11, 14-18 November 2011, Paris, France
. 7. Application to QCD
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13. HCP'11, 14-18 November 2011, Paris, France

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16. HCP'11, 14-18 November 2011, Paris, France
8.Final remarks and conclusion
The self-consistent solutions of the non-homogeneous YM equation and the Dirac equation
in the external YM field is derived in the quasi-classical model when the YM field is assumed to be
in form of the eikonal wave.
2. The quantum theory of the considered model is developed in the quasi-classical approximation.
3. The considered model is solvable when the dimension of the gauge group and assumes
that the fermion and gauge fields have to exist together .
That is an alternative to Glasma model by L.D.McLerran and R.Venugopalan.
4. The relation of the developed model to the generally accepted point of view on the matter
generated in collisions of heavy ions of high energies is considered.
5. The fermion and gauge fields derived in the explicit form allow to develop diagram technique
beyond perturbative consideration.
HCP'11, November 2011, Paris, France