Solution of Dirac equation in external Yang–Mills gauge field

2010

Preprint

The quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. On a basis of the exact solution of the Dirac equation in the SU (N ) gauge field, which is in the eikonal approximation, the Yang-Mills (YM) equations containing the external fermion current are solved. The derived solutions are quantized in the quasi-classical approach. The developed model proves to have the self-consistent solutions of the Dirac and Yang-Mills equations at N ≥ 3. Thereat the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to it self-interaction. The obtained solution are considered in the context of QCD.

“…The transforming the exponent in the same way as it has been done in Ref. [25] (see also Appendix A), we obtain:…”

Section: Fermions In the External Ym Fieldmentioning

confidence: 98%

The Dirac and Gauge Yang-Mills Fields in Self-Consistent Consideration

2010

Preprint

“…Let us apply the results obtained in the previous sections to calculation of a boson mass in terms of the self-consistent quasi-classical model developed in Ref. [10,11]. In this case the convolution in Eqs.…”

Section: Bosonization In Quasi-classical Modelmentioning

confidence: 99%

“…The obtained spectrum is free from the zero point energy. When the confinement phase is governed by the equations of the self-consistent quasi-classical model [10,11] a boson mass is calculated provided that a quark-gluon plasma is bosonated into the lightest bosons (pions).…”

Section: Introductionmentioning

confidence: 99%

Hadronization in SU(N) Gauge Field Theory

Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012)

2012

The bosonization of the strong interacting matter as a process of arising observable hadrons is studied in terms of the phase transition of the second kind. The spectrum of bosons which is free from the zero point energy is derived . The calculated boson mass is found to depend selfconsistently on both the amplitude of a gauge field and quark mass. In the framework of the quasi-classical model[10, 11] a hadron mass is calculated in the case of bosonization into pions.

“…[25] and consists of separating the groups of odd and even terms in the expansion of the exponent (see Ref. [25]). As a result , we obtain:…”

Section: Quasi-classical Model In Su(n) Gauge Field Theorymentioning

confidence: 99%

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

Proceedings of Light Cone 2010: Relativistic Hadronic and Particle Physics — PoS(LC2010)

2010

The quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. On a basis of the exact solution of the Dirac equation in the SU(N) gauge field, which is in the eikonal approximation, the Yang-Mills (YM) equations containing the external fermion current are solved. The derived solutions are quantized in the quasi-classical approach. The developed model proves to have the self-consistent solutions of the Dirac and Yang-Mills equations at N ≥ 3. Thereat the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to it self-interaction. The obtained solution are considered in the context of QCD. Light Cone 2010: Relativistic Hadronic and Particle Physics