Recent Developments in the Nuclear Many-Body Problem

The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities

a r X

i

v

:n u

c

l

-

t h /

1

9

7

v

1

4

S

e

p

2

1

RECENT DEVELOPMENTS IN THE NUCLEAR MANY-BODY PROBLEM R.J.FURNSTAHL Dept.of Physics,Ohio State University,Columbus,OH 43210,USA E-mail:furnstahl.1@osu.edu The study of quantum chromodynamics (QCD)over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem.Recent developments are changing this situation.New ex-perimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD.A common theme is the use of e?ective ?eld theory (EFT)methods,which exploit the separation of scales in physical sys-tems.At low energies,e?ective ?eld theory can explain how existing phenomenol-ogy emerges from QCD and how to re?ne it systematically.More generally,the application of EFT methods to many-body problems promises insight into the an-alytic structure of observables,the identi?cation of new expansion parameters,and a consistent organization of many-body corrections,with reliable error estimates.1Introduction At a fundamental level,atomic nuclei are described by quantum chromodynamics (QCD)with colored quark and gluon degrees of freedom,whose interactions are asymptotically free at short distances.Yet under ordinary conditions,colorless nucleons in a nucleus largely retain their identity.1In the traditional approach to the low-energy nuclear many-body problem,a phenomenological two-nucleon potential is ?t to scattering data and properties of the deuteron,and solutions to the many-body Schr¨o dinger equation for nuclei across the periodic table and nuclear matter are approximated by various sophisticated methods.Three-body forces and meson-exchange currents are added only when required by discrepancies with data.The study and validation of QCD in other contexts over the past quarter century has had relatively little impact on this phenomenology.1Recent developments are changing this situation in two major ways.First,the

nuclear many-body problem has become the QCD many-body problem,involving explorations of phenomena throughout the phase diagram of QCD.Second,e?ective ?eld theory (EFT)methods are being used to build bridges from QCD to tradi-tional nuclear many-body phenomenology.The phrase “e?ective theory”has often denoted a model used because one couldn’t solve the underlying theory.In contrast,an EFT is a ?eld theory that reproduces the results of an underlying theory in a systematic and model-independent way,but in a limited domain.

It would be impractical to make a complete survey of this broad range of activity,so we will instead present a coarse-grained tour with selected stops.Many more details are available in the cited references.We will start with “teasers”from two of the many new frontiers in exploring the QCD phase diagram,many-body physics at small x and color superconductivity.New insights into established approaches within the traditional framework and how successful phenomenology emerges from low-energy QCD are considered next.Finally,we give an example of how new ideas for attacking many-body problems arise from applying the EFT perspective.furnstahl˙talk:submitted to World Scienti?c on February 8,20081

The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities

Figure1.The conjectured phase diagram of QCD(see Ref.3for details).

2Exploring the QCD Phase Diagram

Quantum chromodynamics(QCD)is a gauge theory of SU(3)color charges,with quarks and gluons as the fundamental degrees of freedom.It has many analogies to quantum electrodynamics(QED),but important di?erences follow from the non-abelian structure.In particular,gluons carry the color charge and interact with each other.Two prominent consequences are asymptotic freedom(the interaction becomes weak at high energies/short distances)and color con?nement(observed hadrons have no net color charge).Quarks come in six varieties,called?avors,with masses that are very small compared to the relevant QCD scale(up,down)or very large(charm,top,bottom).The strange quark mass is somewhere in the middle; whether it should be considered heavy or light has an important in?uence on the phase structure of QCD.

Figure1is a conjectured phase diagram for QCD.The axes here are the tem-perature and the chemical potential for baryon number.The traditional nuclear many-body problem lives in the small black blob at low temperature with chemical potential near one GeV.But now the nuclear many-body problem encompasses the entire plane and can more correctly be termed the QCD many-body problem.Even the physical vacuum(T=0,µB=0)is an extraordinarily complex,coherent many-body medium characterized by nonperturbative quark and gluon condensates.2 One of the main tasks of the new nuclear many-body problem is to explore the phase structure in Fig.1,such as the expected decon?nement and chiral symmetry restoration phase transitions.These transitions are predicted by lattice simula-tions;however,the simulations are restricted at present to zero chemical potential. furnstahl˙talk:submitted to World Scienti?c on February8,20082

The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body pr …… 此处隐藏：35525字，全部文档内容请下载后查看。喜欢就下载吧 ……