Collective Quantum Fields

Abstract A general quantum field theory of collective excitations is presented for many‐body systems. Lagrangians involving fundamental particles are transformed to collective fields exactly via Feynman path integrals. Graphically, this amounts to a complete resummation of the perturbation series without the danger of double counting. Plasma and pairing effects provide special examples corresponding to mutually complementary transformations. Bose and Fermi systems can be treated on equal footing. The methods are illustrated by giving the exact collective Lagrangian for the BCS model and approximate ones for type II superconductors and 3 He.