Contents: Introduction; From particles to fields; Quantising the classical field; Second quantisation; Representation of operators; Tight-binding and the Mott Transition; Quantum magnetism and the Ferromagnetic chain; Quantum Antiferromagnetism; Bogoliubov theory of weakly interacting Bose gas; Fyenman path integral; Statistical mechanics and semi-Classics; Applications of the feynman path integral; Double well potential: tunneling and instantons; Coherent states; Many-body (coherent state) path integral; Applications and connections; Weakly interacting electron gas: Plasma theory; Random phase approximation; Bose-Einstein condensation; Superfluidity; Cooper instability;: BCS Superconductivity; Field theory of superconductivity; Superconductivity and gauge invariance. |