Results on Interacting Bose Gases

In this talk recent results in the quantum theory of interacting Bose gases are reviewed. Use is made of

1. a representation of Bose gases as a kind of scalar field theory resulting from a Hubbard-Stratonovich transformation;
2. Ginibre’s Brownian loop representation;
3. an interpolation in the number N of atom species; and
4. simplifications appearing in various limiting regimes.

The purpose is to study phenomena related to Bose-Einstein condensation and properties of polymer chains (N → 0). Some novel support for the conjecture that λ|φ|^{4}_{d}-theory in d ≥ 4 dimensions is non-interacting will also be described.