Quasi-Classical Model in SU(N) Gauge Field Theory

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Quasi-Classical Model in SU(N) Gauge Field
Theory A.V.KOSHELKIN
Moscow Institute for
Physics and Engineering
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CONTENTS 1.      Introduction. 2. Statement of
Problem and Main Goal. 3. Self-Consistent
Solution. 4. Fermion and Gauge Field in
Developed Model. 5. Application to QCD. 6.
Conclusion.
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1.      Introduction.


PEOPLE C.N.Yang, R.L.Mills, Rev. 51 461
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(1976). P.Sikivie, N.Weiss, Phys. Rev. 20 487
(1979). R.Jackiw, L.Jacobs, C.Rebbi, Phys. Rev.
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T.Shreecharan. e-Print arXiv0912.3993het-th. D
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067701. A.Slavnov, L.Faddeev, Introduction to
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Nucl.Phys. 76 (1966) 588. and so on, so on
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2.Statement of Problem and Main Goal.
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Key Approximations
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 .
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The Yang-Mills equation


WE ASSUME
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The Dirac equation


Provided
that
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SOLUTION IS

(Koshelkin,Phys.Lett.
,B683 (2010) 205)
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3. Self-Consistent Solution.
a) Gauge field
b) Fermion field
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c) Relation equations
(Koshelkin,Phys.Lett.,B696 (2011) 539)
The problem is solvable when the
dimension of the gauge group .
Thereat, the currents generated by fermions and
gauge field exactly compensate each other.
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4. 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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Fermion effective mass.


IN EQUILIBRIUM
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. 5. Application to QCD
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• 6.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.