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
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
SN - 0010-3616
VL - 258
SP - 675
EP - 695
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
ER -