In their paper, Titulaer and Glauber state

The results [...] are derived only for fields with positive-definite P functions. Those are, in fact, precisely the quantum fields which may be described in a natural way as possessing classical analogs.

The $P$ function mentioned here is the Glauber-Sudarshan P representation. In the paper the authors shows that for $P \ge 0$ correlation functions follow a hierarchy of inequalities and, apparently, from these inequalities it follows that the state described by $P$ has a classical analog.

However, I fail to see how one can draw this conclusion, especially since this point is not further elucidated. So what is the argument I am missing or is there a better reference to see that positive $P$ functions correspond to classical states (or the often stated converse: negative $P$ indicate non classical behaviour)?

  • $\begingroup$ You do appreciate "classical analog" states is a synonym for just generalized coherent states ("Schrodinger wave packets"), right? $\endgroup$ Apr 15, 2021 at 17:30
  • $\begingroup$ @CosmasZachos I appreciate that this was new to me. Still, I fail to see that generalised coherent states necessarily produce positive P's and I still don't see the connection that is made in the paper, or more generally why Glauber defines "positive P are classical". $\endgroup$
    – manthano
    Apr 16, 2021 at 5:08
  • 1
    $\begingroup$ W Schleich’s textbook has a good review of this fact. $\endgroup$ Apr 16, 2021 at 10:45


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