Chiral symmetry in nuclei

Effective field theory is considered to provide a highly useful framework for connecting nuclear physics with the symmetries and dynamics of the underlying theory of strong interactions, QCD. Of many issues that are of great current interest in this domain, I concentrate here on two: (1) A new class of ab initio calculations of observables in two-nucleon systems; (2) Attempts to extend chiral perturbation calculations to higher-order terms.     

Chiral symmetry in nuclei and nuclear matter

We discuss a model for hadrons based on chiral symmetry, Hadronic masses are generated via spontaneous symmetry breaking. Within this model we investigate nuclear matter and finite nuclei. Since the model is SU_F(3)-symmetric we are also able to investigate hypernuclei. Numerical results in comparison with experimental data are presented.     

Three-body forces and many-body dynamics

Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations. The text was submitted by the author in English.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Pyroelectricity and the strength of many-body forces

The linear relation between pyroelectric coefficient and specific heat for ZnO is interpreted in terms of rigid ions. Some other materials behave differently and exhibit stronger pyroelectricity. This is interpreted as due to many-body forces. Conditions favourable for pyroelectricity are thereby suggested.     

Range of forces and broken symmetries in many-body systems

It is argued that for a many-body system with short range forces the commutators between local operators at different times will be fast decreasing for large spatial separations.This allows the adaptation of many discussions in relativistic field theories to the case of a many-body system with short range forces. In particular one has the result that a spontaneous breakdown in symmetry implies the existence of excitations of arbitrarily small energy. However this result has essentially only one application: We know that the Galilei invariance is always broken (in a medium of finite density). Therefore one concludes that in a many-body system with short range forces there can never be an energy gap.Supported by the National Science Foundation.     

Chiral symmetry breaking in QCD

By applying bifurcation theory to a truncated Dyson-Schwinger equation for the quark propagator in massless QCD, we show that dynamical symmetry breaking occurs at a certain critical value of the coupling constant. Essential ingredients are (a) an effective dynamical mass for the gluon, and (b) a running coupling constant.     

Chiral symmetry and nucleon-nucleon scattering

The contributions of the minimal chiral two-pion exchange nucleon-nucleon potential for some selected observables are studied by means of the variable phase method. We conclude that chiral symmetry is responsible for important cancellations, which are related to those occurring in pion-nucleon scattering.     

Chiral symmetry breaking in SQCD

Using a spectral function sum rules approach, we derive some constraints among the Goldstone parameters, the lowest dimension vacuum condensates and the mass of the chiral matter superfield in supersymmetric QCD (SQCD). These relations are consistent with previous results on SQCD and complement them.     

Chiral symmetry in quarkyonic matter

The 1/N _c expansion classifies nuclearmatter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, $\left\langle {\bar \psi exp\left( {2i\mu _q z\gamma ^0 \gamma ^z } \right)\psi } \right\rangle$ . An extension to multiple chiral spirals is also briefly discussed.     

Chiral symmetry and excited baryons

An approach to baryons in the framework of the microscopic generalized Nambu-Jona-Lasinio chiral potential quark model is considered and quite general arguments are given in favor of the effective restoration of the chiral symmetry in excited baryons. The text was submitted by the authors in English.     

Chiral symmetry and lattice QCD

Four lectures about chiral symmetry and dynamical fermions in QCD. 1) Chiral symmetry in continuum QCD with an eye toward lattice simulations. 2) Lattice fermions with exact chiral symmetry: staggered fermions, fermions in five dimensions, chiral fermions in four dimensions. 3) A typical lattice simulation from beginning to end: the simulation algorithm, designing observables to measure some desired quantity, analyzing the data. 4) Recent lattice results relevant to chiral symmetry: a mini-review.     

Chiral symmetry and functional integral

The change in the fermionic functional integral measure under chiral rotations is analyzed. Using the ζ-function method, the evaluation of chiral Jacobians to theories including nonhermitian Dirac operators D, can be extended in a natural way. (This being of interest, for example, in connection with the Weinberg-Salam model or with the relativistic string theory.) Results are compared with those obtained following other approaches, the possible discrepancies are analyzed and the equivalence of the different methods under certain conditions on D is proved. Also shown is how to compute the Jacobian for the case of a finite chiral transformation and this result is used to develop a sort of path-integral version of bosonization in d = 2 space-time dimensions. This result is used to solve in a very simple and economical way relevant d = 2 fermionic models. Furthermore, some interesting features in connection with the θ-vacuum in d = 2,4 gauge theories are discussed.     

原子核的四面体对称性

除了几个幻数核呈球形外,原子核大都是变形的,例如椭球形。现代核物理实验已发现,原子核可以呈“梨形”形变,即具有反射不对称性。理论研究预言,原子核还可能具有“金字塔”形变,即四面体对称性,而实验上还未找到原子核的这种新对称性。文章从强相互作用量子多体体系的对称性及其破缺的基本规律出发,阐明原子核四面体形变的形成机制,并介绍其理论描述。同时讨论寻找四面体形变原子核的基本方法和最新实验研究进展。     

Pseudospin symmetry in finite nuclei

The pseudospin symmetry (PSS) is an important feature of the nuclear structure. Most of the authors working in this field at present consider the PSS as an approximate symmetry, although there exist certain essential differences in opinions about the particularities of its realization. We have shown that the PSS in the nucleus is strongly related to the spin-orbit interaction and, consequently, to the spin symmetry (SS). We conclude that the PSS, as well as the SS, can be studied appropriately in the framework of the relativistic formalism. The text was submitted by the authors in English.     

Chiral symmetry breaking in dense matter

The quark condensate in nuclear matter is studied. We relate it to the nuclear sigma commutator, and then treat it as sigma commutator for quasi- particles in a self-consistent way. We find that the deviation from the linear expression is large at high density. Received: 20 November 1997 / Revised version: 24 February 1998 / Published online: 16 September 1998