  The Glauber-Sudarshan $P$-representation is used in quantum optics to
distinguish between semi-classical and genuinely quantum electromagnetic
fields. We employ the analog of the $P$-representation to show that the
violation of the Cauchy-Schwarz inequality for the second-order correlation
function is a proof of entanglement between identical massive bosons. The
presented derivation is valid both in systems with fixed and fluctuating number
of particles. Thanks to the recent advances in techniques of detecting
positions of separate particles, the violation of the Cauchy-Schwarz inequality
can be used as a simple entanglement criterion in various many-body quantum
systems.
