  The truncated Wigner approximation (TWA) enables us to calculate bosonic
quantum many-body dynamics while accounting for the effects of quantum
fluctuations. In this work, we formulate the TWA for bosonic Markovian open
quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)
equation from the coherent-state path-integral approach using the Wigner
function. We derive an analytical expression for the GKSL equation in the TWA
where we consider a bosonic system with an arbitrary Hamiltonian with jump
operators that do not couple different states. We numerically confirm that the
time evolution of physical quantities and the non-equal time correlation
functions obtained in our formulation agree well with the exact ones in the
numerically solvable models.
