## Equivalence of two definitions of the effective mass of a polaron    [PDF]

Elliott H. Lieb, Robert Seiringer
Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Froehlich polaron model. These are: 1. the mass defined by the low momentum energy \$E(P) \approx E(0)+P^2/2M\$ of the translation invariant system constrained to have momentum \$P\$ and 2. the mass \$M\$ of a simple particle in an arbitrary slowly varying external potential, \$V\$, described by the nonrelativistic Schroedinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same \$V\$.
View original: http://arxiv.org/abs/1304.1780