Gauge invariant gluon spin operator for spinless nonlinear wave solutions

Abstract

We consider non-linear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU (2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of a static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered non-linear wave type solutions have common features: presence of the mass scale parameter, non-vanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

On microscopic structure of the QCD vacuum

“…First of all, note that a system of separated stationary generalized Wu-Yang monopoles and antimonopoles can not be stable due mutual attraction between the monopole and antimonopole. In addition, despite on the quantum stability of a sinlge stationary spherically symmetric monopole, the solution is rather classically unstable with respect to small axially-symmetric field deformations [14]. This implies that axially-symmetric solutions are more preferable as candidates for the vacuum.…”

“…Usually one expects that introducing time dependent color fields as vacuum makes worse the vacuum stability since the color electric field leads to an imaginary part of the effective action as well [23]. Surprisingly, it has been found that non-linear plane wave solutions make the problem of vacuum stability more soft, in a sense, that an equation for the unstable modes is very similar to the equation for an electron in the periodic potential [14]. This gives a hint that one can find a proper stationary periodic wave type solution which provides a stable vacuum.…”

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

“…Let us first describe the main properties of the stationary spherically symmetric monopole solution [30]. Due to conformal invariance of the Yang-Mills theory the static soliton solutions do not exist in agreement with the known Derrick's theorem.…”

“…Due to conformal invariance of the Yang-Mills theory the static soliton solutions do not exist in agreement with the known Derrick's theorem. It is somewhat unexpected that a pure QCD admits a regular stationary monopole like solution [30]. The solution is described by a simple ansatz which generalizes the static Wu-Yang monopole solution (in spherical coordinates (r, θ, ϕ))…”

“…A careful analysis shows that in spite of several attractive properties of such solutions the non-linear plane waves are unstable against vacuum gluon fluctuations. In Section IV we consider quantum stability of a recently proposed stationary monopole solution [30] which represents a system of a static Wu-Yang monopole interacting to off-diagonal components of the gluon field. We have proved that such a generalized monopole solution provides a stable vacuum field background in the effective action of QCD in one-loop approximation.…”