English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This article reports an explicit function form for confining classicalYang-Mills vector potentials and quantum fluctuations around the classicalfield. The classical vector potential, which is composed of a confininglocalized function and an unlocalized function, satisfies the classicalYang-Mills equation. The confining localized function contributes to the Wilsonloop, while the unlocalized function makes no contribution to this loop. Theconfining linear potential between a heavy fermion and antifermion is due to(1) the Lie algebra and (2) the form of the confining localized function whichhas opposite signs at the positions of the particle and antiparticle along theWilson loop in the time direction. Some classical confining parts of vectorpotentials also change sign on inversion of the coordinates of the axisperpendicular to the axis joining the two particles. The localized parts of thevector potentials are squeezed around the axis connecting the two particles,and the string tension of the confining linear potential is derived. Quantumfluctuations are formulated using a field expression in terms of local basisfunctions in real spacetime. The quantum path integral gives the Coulombpotential between the two particles in addition to the linear potential due tothe classical fields.

Example of an explicit function for confining classical Yang-Mills fields with quantum fluctuations in the path integral scheme