Eective Field Theory

James G. Glimm, Arthur M. Jaffe

Zygmunt M. Galasiewicz

The investigation has been based on Hamiltonian quadratic in Fermi amplitudes or linear in operators representing amplitude and phase of condensate of pair (parallel spins).The latter represents the energy of a \spin" 1=2 L in some eective eld.Simple variational procedure gives for anisotropic ABM and \polar" phases single particle energy with a suitable form of energy gap.Amplitude and phase oscillations are connected with frequencies != 0; 2 .The rst one represents Goldstone{Anderson mode.\Spins" dependence on time ( L(i) (t) = Rij(t) L(j) (0)) is given by rotation matrix Rij(t) used in He 3 {B theory.Here Rij describes rotation of a \spin" around the eective eld.

Newton C. A. da Costa, Francisco Antônio Dória

Asao Arai

Aquantum system of aDirac particle -arelativistic charged particle with spin 1/2 -interacting with the quantum radiation field is considered and an eective particle Hamiltonian is derived as ascaling limit of the total Hamiltonian of the system.

Howard M. Georgi

T. P. Polak

The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied.An articial magnetic eld is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents.A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations eects of the fermion mediated interaction between bosons.In consequence the eective interaction between bosons can change the magnitude and sign.This provides possible explanations of the bosonic coherence loss observed experimentally in the time of ight and peak width experiments.