What Is the Lagrangian Counting?

M. J. de la Plata, L. L. Salcedo

The Feynman rules to be used with the effective action line and vertices are derived. It is argued that they are a natural extension of the ordinary Feynman rules (in terms of bare line and vertices) to the case of perturbing a non quadratic action. It is shown how the extended rules can be used to derive diagrammatic identities, to obtain low density expansions in many-body problems and to avoid double-counting of vacuum contributions when effective Lagrangians are used.

Alexander Komech

Hagen M. Kleinert

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 3He.

DONALD A. DUNN

W. Vincent Liu

We consider the low-energy collective excitations at finite temperature of Bose–Einstein condensed gases (and liquids as well). A most general model-independent effective Lagrangian is written down according to a prescription obtained from the breakdown of the global symmetry U(1). To show how the theory predicts easily, we derive the momentum and temperature dependence of the damping of excitations by means of power counting as an example.