TY - JOUR

T1 - The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field

T2 - I. The lower bound

AU - Lieb, Elliott H.

AU - Loss, Michael

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2005/9

Y1 - 2005/9

N2 - The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, was accomplished decades ago in the framework of non-relativistic quantum mechanics, . This result did not take account of interactions caused by magnetic fields, however, (the spin-spin interaction, in particular) or of the quantized nature of the electromagnetic field. Recent progress has made it possible to undertake such a proof in the context of non-relativistic QED. This paper contains one part of such a proof by giving a lower bound to the free energy that is proportional to the number of particles and which takes account of the fact that the field, unlike the particles, is never confined to a finite volume. In the earlier proof the lower bound was a 'two line' corollary of the 'stability of matter'. In QED the proof is much more complicated.

AB - The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, was accomplished decades ago in the framework of non-relativistic quantum mechanics, . This result did not take account of interactions caused by magnetic fields, however, (the spin-spin interaction, in particular) or of the quantized nature of the electromagnetic field. Recent progress has made it possible to undertake such a proof in the context of non-relativistic QED. This paper contains one part of such a proof by giving a lower bound to the free energy that is proportional to the number of particles and which takes account of the fact that the field, unlike the particles, is never confined to a finite volume. In the earlier proof the lower bound was a 'two line' corollary of the 'stability of matter'. In QED the proof is much more complicated.

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U2 - 10.1007/s00220-005-1365-y

DO - 10.1007/s00220-005-1365-y

M3 - Article

AN - SCOPUS:22944453673

VL - 258

SP - 675

EP - 695

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -