Stability and absence of binding for multi-polaron systems

We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for Na parts per thousand yen2 polarons. Frohlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling , and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U < 2 alpha, stability of matter does hold for U > 2 alpha, that is, the ground state energy per particle has a finite limit as N -> a. (ii) There is no binding of any kind if U exceeds a critical value that depends on alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.