Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ρ_{00} for ϕ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to ϕ meson's spin alignment. We propose that the local correlation or fluctuation of ϕ fields is the dominant mechanism for the observed ϕ meson's spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ρ_{00} agrees with STAR's data. We further predict the azimuthal angle dependence of ρ_{00} which can be tested in future experiments.

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 ρ00 for vector mesons on a solid ground. Within the theory we formulate ρ00 for φ mesons into a factorization form in separation of momentum and spacetime variables. We argue that the main contribution to ρ00 at lower energies should be from the φ 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 φ meson wave function between the φ field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to ρ00 are all in squares of fields that are nonvanishing even if the fields may strongly fluctuate in spacetime. The fluctuation of strong force fields can be extracted from ρ00 of unflavored vector mesons as links to fundamental properties of quantum chromodynamics.