Many-body Problem in Quantum Field Theory

Effective Field Theory and the Nuclear Many Body Problem

We review many body calculations of the equation of state of dilute neutron matter in the context of effective field theories of the nucleon-nucleon interaction. PACS. 21.65.+f Nuclear Matter – 24.85.+p QCD in Nuclei

Convexity and the quantum many-body problem

We recall some properties of convex functions and, in particular, of the sum of the largest eigenvalues of a Hermitian matrix. From these properties a new estimate of an arbitrary eigenvalue of a sum of Hermitian matrices is derived, which in turn is used to compute an approximate associated spectral projector. These estimates are applied for the first time to explain generic spectral features ...

Quantum Many–Body Problems and Perturbation Theory

We show that the existence of algebraic forms of exactly-solvable A−B− C−D and G2, F4 Olshanetsky-Perelomov Hamiltonians allow to develop the algebraic perturbation theory, where corrections are computed by pure algebraic means. A classification of perturbations leading to such a perturbation theory based on representation theory of Lie algebras is given. In particular, this scheme admits an ex...

Nonequilibrium Relativistic Quantum Many-Body Theory

Three-Body Interactions in Many-Body Effective Field Theory

A general principle of any effective low-energy theory is that if a system is probed or interacts at low energies, resolution is also low, and fine details of what happens at short distances or in high-energy intermediate states are not resolved [ 1]. In this case, it is easier and more efficient to use low-energy degrees of freedom for low-energy processes. The short-distance structure can be ...