Relativistic Spin Dynamics for Vector Mesons

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 spacetime 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 that are nonvanishing even if the fields may strongly fluctuate in spacetime. The fluctuation of strong force fields can be extracted from rho 00 of unflavored vector mesons as links to fundamental properties of quantum chromodynamics.