Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD

The problem of the existence of a stable vacuum field in pure QCD is revised. Our approach is based on using classical stationary nonlinear wave type solutions with an intrinsic mass scale parameter. Such solutions can be treated as quantum-mechanical wave functions describing massive spinless states in quantum theory. We verify whether nonlinear wave type solutions can form a stable vacuum field background within the framework of the effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions that are stable against quantum gluon fluctuations.

Figure 1

Stationary spherically symmetric monopole solution in the numeric domain $(0\le r\le 8\pi ,0\le t\le 2\pi )$, with $c_0=-0.251$, $a_0=0.84175$, and $A_0=0.6405$.

Figure 2

Eigenfunction ${\mathrm{\Psi }}_2^2$ for the ground state with the lowest eigenvalue ${\lambda }_I=0.0531$, with $a_0=0.895$, $A_0=0.615$, $g=1$, $M=1$, $0\le r\le 6\pi$, $0\le t\le 2\pi$, and $0\le \theta \le \pi$.

Figure 3

Solutions to Eq. (42): the functions ${\mathrm{\Psi }}_1^3(r,t)$ (a) and ${\mathrm{\Psi }}_2^1(r,t)={\mathrm{\Psi }}_3^2(r,t)$ (b) corresponding to the eigenvalue $\lambda =0.014218$, with $a_0=0.895$, $A_0=0.615$, $M=1$, $0\le r\le 6\pi$, and $0\le t\le 2\pi$.

Figure 4

Lowest eigenvalue dependence $\lambda (L)$ on the radial size $L$ of the numerical domain.

Figure 5

Solution $f_2^2$ of system (I), $f_3^1(r,t)=-f_2^2(r,t)$, for ${\lambda }_I=0.0586$, with $0\le r\le 6\pi$ and $0\le t\le 2\pi$.

Figure 6

Solution of system (III) for $\lambda =0.0293$, with $0\le r\le 6\pi$ and $0\le t\le 2\pi$: (a) $f_1^3(r,t)$; (b) $f_2^1(r,t)=f_3^2(r,t)$.