Justification of c-number substitutions in bosonic hamiltonians

Elliott H. Lieb, Robert Seiringer, Jakob Yngvason

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.

Original languageEnglish (US)
Article number080401
JournalPhysical review letters
Issue number8
StatePublished - Mar 4 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


Dive into the research topics of 'Justification of c-number substitutions in bosonic hamiltonians'. Together they form a unique fingerprint.

Cite this