Equivalence of two definitions of the effective mass of a polaron

Abstract

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 $V$.

10 pages

References in corpus (2)

• Renormalized Electron Mass in Nonrelativistic QED
• Effective dynamics for particles coupled to a quantized scalar field

Cited by in corpus (6)

• Divergence of the effective mass of a polaron in the strong coupling limit
• Effective mass of the polaron -- revisited
• The Polaron at Strong Coupling
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Polaron models with regular interactions at strong coupling
• Ground State of the Polaron Hydrogenic Atom in a Strong Magnetic Field