The <FONT FACE=Symbol>d</font> Expansion and the Principle of Minimal Sensitivity

Abstract

The -expansion is a nonperturbative approach for eld theoretic models which combines the techniques of perturbation theory and the variational principle. Di erent w ays of implementing the principle of minimal sensitivity to the -expansion produce in general di erent results for observables. For illustration we use the Nambu Jona-Lasinio model for chiral symmetry restoration at nite density and compare results with those obtained with the Hartree-Fock approximation.The standard application of the linear -expansion 1 to a theory with action S starts with an interpolation de ned by S = 1 , S 0 + S, where S 0 is the action of a solvable theory. The action S interpolates between the solvable S 0 when = 0 and the original S when = 1. Since S 0 is quadratic in the elds, arbitrary parameters with mass dimensions are required for dimensional balance. At the end one sets = 1 xing according to the principle of minimal sensitivity PMS 2 which requires a physical quantity to satisfyWithin this method, the general procedure is to apply the PMS directly to each di erent quantity o f i n terest so as to adjust to the di erent energy scales of the theory 2 . A natural question which arises at this point is the uniqueness of the value of since di erent p h ysical quantities might generate di erent v alues for the optimal . Of course this would not be catastrophic if the spread of the values of determined from di erent observables were not too large.Alternatively, one could select only one among those

Recent Progress in Quantum Hadrodynamics

“…Other phenomena such as (σωγ) mixing, (ρω) mixing, charge-symmetry breaking, and the production of (e + e − ) pairs to probe the quark-gluon plasma are discussed in [Kr92,Li95a,Li95b].…”

“…Relativistic analyses of the photonuclear reactions (γ, p) and (γ, π − p) are discussed in [Lo92,He94,Jo94]. Other phenomena such as (σωγ) mixing, (ρω) mixing, charge-symmetry breaking, and the production of (e + e − ) pairs to probe the quark-gluon plasma are discussed in [Kr92,Li95a,Li95b].…”

High temperature resummation in the linearδexpansion

“…The optimized linear δ-expansion is an alternative nonperturbative approximation which has been successfully used in a plethora of different problems in particle theory [15,[17][18][19], quantum mechanics [20,21] statistical physics [22], nuclear matter [23] and lattice field theory [24]. One advantage of this method is that the selection and evaluation (including renormalization) of Feynman diagrams are done exactly as in ordinary perturbation theory using a very simple modified propagator which depends on an arbitrary mass parameter.…”