Exact Results in Quantum Theory

We study the homogeneous mean-field Bose gas at temperatures proportional to the critical temperature of its Bose-Einstein condensation phase transition. We establish a trace norm approximation for the grand canonical Gibbs state, providing the first rigorous justification of Lee and Yang's extension of Bogoliubov theory to finite temperatures. This is joint work with A. Deuchert (Virginia Tech) P.T. Nam (LMU Munich).