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