Equivalence of Two Definitions of the Effective Mass of a Polaron

Elliott H. Lieb, Robert Seiringer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈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 Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.

Original languageEnglish (US)
Pages (from-to)51-57
Number of pages7
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jan 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Dressed particle
  • Effective mass
  • Polaron
  • Quantum field theory


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