Bose-Einstein Condensation and Spontaneous Symmetry Breaking

Abstract

After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein Condensation is presented. The proof is based on a rigorous validation of Bogoliubov's $c$-number substitution for the $\mathbf{k}=0$ mode operator $a_0$.

arXiv commentContribution to the proceedings of the 21st Max Born Symposium, Wroclaw, Poland, June 26--28, 2006. (References added. To be published in Reports on Mathematical Physics.)

References in corpus (3)

• Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
• Justification of c-Number Substitutions in Bosonic Hamiltonians
• Equivalence of Bose-Einstein condensation and symmetry breaking

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• Quantum Enhancement of Thermalization
• Landau superfluids as non equilibrium stationary states
• Ground state properties of the disordered spin-one Bose-Hubbard model: a stochastic mean-field theory study