Gouranga C. Nayak

General form of the color potential produced by color charges of the quark

A bstractConstant electric charge e satisfies the continuity equation ∂μjμ(x) = 0 where jμ(x) is the current density of the electron. However, the Yang-Mills color current density jμa(x) of the quark satisfies the equation Dμ[A]jμa(x) = 0 which is not a continuity equation (∂μjμa(x) ≠ 0) which implies that a color charge qa(t) of the quark is not constant but it is time dependent where a = 1,2, . . .8 are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by

General form of color charge of the quark

{\varPhi^a}(x)=A_0^a\left( {t,\mathrm{x}} \right)=\frac{{{q^b}\left( {t-\frac{r}{c}} \right)}}{r}{{\left[ {\frac{{\exp \left[ {g\int {dr\frac{{Q\left( {t-\frac{r}{c}} \right)}}{r}} } \right]-1}}{{g\int {dr\frac{{Q\left( {t-\frac{r}{c}} \right)}}{r}} }}} \right]}_{ab }}

Proof of factorization using background field method of QCD

where dr integration is an indefinite integration,

Proof of Factorization of Fragmentation Function in Non-Equilibrium QCD

{Q_{ab }}\left( {{\tau_0}} \right)={f^{abd }}{q^d}\left( {{\tau_0}} \right),\;r=\left| {\overrightarrow{x}-\overrightarrow{X}\left( {{\tau_0}} \right)} \right|,{\tau_0}=t-\frac{r}{c}

Factorization of soft and collinear divergences in non-equilibrium quantum field theory

is the retarded time, c is the speed of light,

Dark matter production at the LHC from black hole remnants

\overrightarrow{X}\left( {{\tau_0}} \right)

String theory at LHC using Higgs production and decay from string balls

is the position of the quark at the retarded time and the repeated color indices b, d(= 1, 2, . . . 8) are summed. For constant color charge qa we reproduce the Coulomb-like potential

Renormalization group equation and QCD coupling constant in the presence of SU(3) chromo-electric field

{\varPhi^a}(x)=\frac{{{q^a}}}{r}

Light-Like Wilson Line in QCD Without Path Ordering

which is consistent with the Maxwell theory where constant electric charge e produces the Coulomb potential

String theory at LHC using top quarks from string balls

\varPhi (x)=\frac{e}{r}