We investigate the dynamics and mass spectra of charged pseudoscalar (${\pi }^{+}$) and vector (${\rho }^{+}$) mesons in a background magnetic field at finite temperature using the two-flavor Nambu-Jona–Lasinio model. By employing a quark propagator that isolates the Schwinger phase from its Landau level expansion, we formulate an analytically controlled phase-space framework utilizing the Wigner-Weyl transform and the Moyal star product. This approach enables the algebraic diagonalization of the Bethe-Salpeter equations for composite states with asymmetric fractional constituent charges. For the pseudoscalar channel, we analytically verify the exact cancellation between the dynamical random phase approximation spatial sum rules and the vacuum gap equation. This identity preserves the generalized Goldstone theorem, causing the ${\pi }^{+}$ pole mass to track the kinematic zero-point energy drift at order of $eB$. In the vector channel, our full phase-space evaluation reveals that the Zeeman spin-splitting emerges dynamically from microscopic threshold truncations governed by the chiral Dirac algebra. Notably, we find that the tachyonic instability of the spin-aligned ${\rho }^{+}$ state is quenched. The magnetic catalysis of the chiral condensate drives the continuum threshold ($2M$) upwards, overtaking the Zeeman attraction and preventing vector meson condensation within this mean-field framework. Furthermore, finite-temperature evaluations show a monotonic thermal suppression of the meson masses driven by Pauli blocking, yet all modes remain bound without undergoing Mott dissociation prior to chiral symmetry restoration.

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• Quark matter
• Quark model