Journal of Statistical Physics

, Volume 154, Issue 1–2, pp 51–57 | Cite as

Equivalence of Two Definitions of the Effective Mass of a Polaron

  • 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 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.


Polaron Effective mass Quantum field theory Dressed particle 



Partial financial support by U.S. NSF grant PHY-0965859 (E.H.L.), the Simons Foundation (# 230207, E.H.L.) and the NSERC (R.S.) is gratefully acknowledged.


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Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.Departments of Mathematics and Physics, Jadwin HallPrinceton UniversityPrincetonUSA
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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