  We propose a relativistic theory for spin density matrices of vector mesons
based on Kadanoff-Baym equations in the closed-time-path formalism. The theory
puts the calculation of spin observables such as the spin density matrix
element $\rho_{00}$ for vector mesons on a solid ground. Within the theory we
formulate $\rho_{00}$ for $\phi$ mesons into a factorization form in separation
of momentum and space-time variables. We argue that the main contribution to
$\rho_{00}$ at lower energies should be from the $\phi$ fields that can
polarize the strange quark and antiquark in the same way as electromagnetic
fields. The key observation is that there is correlation inside the $\phi$
meson wave function between the $\phi$ field that polarizes the strange quark
and that polarizes the strange antiquark. This is reflected by the fact that
the contributions to $\rho_{00}$ are all in squares of fields which are
nonvanishing even if the fields may strongly fluctuate in space-time. The
fluctuation of strong force fields can be extracted from $\rho_{00}$ of
quarkonium vector mesons as links to fundamental properties of quantum
chromodynamics.

High Energy Physics - Phenomenology;Nuclear Theory