Hamiltonian reduction of theU EM(1) gauged three flavour WZW model

The three-flavour Wess-Zumino model coupled to electromagnetism is treated as a constraint system using the Faddeev-Jackiw method. Expanding into series of powers of the Goldstone boson fields and keeping terms up to second and third order we obtain Coulomb-gauge hamiltonian densities.     

Dynamical supersymmetry breaking in supersymmetric QCD

The massless limit of supersymmetric QCD with $\text{N}{}_{\mathrm{?}}$ flavors and N colors is analyzed in detail. For $\text{N}{}_{\mathrm{?}}\text{< N}$ there is a unique superpotential which might be generated by non-perturbative effects. We show that it indeed appears, thus violating the non-renormalization theorems. For $\text{N}{}_{\mathrm{?}}\text{= N ? 1}$ instantons produce the superpotential. For $\text{N}{}_{\mathrm{?}}\text{< N ? 1}$ it is again generated, provided that a mild assumption about the dynamics of pure supersymmetric gauge theories is correct. For $\text{N}{}_{\mathrm{?}}\text{? N}$ no invariant superpotential exists; the classical vacuum degeneracy is a property of the full quantum theory. When a small quark mass term is added to the theory $\text{(}\text{for}\text{N}{}_{\mathrm{?}}\text{< N), N}$ supersymmetric ground states, identified with those found by Witten exist. As m → 0 these N vacua wander to infinity, leaving the massless theory without a ground state.     

Convergence of theU(1)4 lattice gauge theory to its continuum limit

It is shown that in four space-time dimensions the compactU(1) lattice gauge theory with general energy function converges to a renormalized free electromagnetic field on the current sector as the lattice spacing approaches zero, provided the coupling constant is sufficiently large. For the Wilson energy function, it is possible, by judicious choice of the Gibbs state, to get convergence for arbitrary coupling strengths. Furthermore, for all but a countable number of values of the coupling constant, the limit exists and is independent of the particular state chosen to define the lattice model.This research was supported in part by an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship and in part by N.S.F. Grant Nos. DMS 84-01997 and DMS-8610730(1)     

Is theU(1) axial symmetry restored above theSU(L) ⊗SU(L) chiral transition?

Zeitschrift für Physik C Particles and Fields - We discuss an effective Lagrangian model in which theU (1) chiral symmetry is restored above theSU (L) ?SU (L) chiral phase transition (L...     

On stability of solutions of theU(N) chiral model in two dimensions

We discuss the stability properties of classical solutions of theU(N) sigma models in two Euclidean dimensions. We show that all nontrivial solutions are unstable. For a general case we exhibit one mode of instability; in some special cases (corresponding to a grassmannian solution and an instantonic grassannian embedding) we exhibit two such independent modes.     

Flavor mixing in the low energy hadron dynamics: Interplay of theSU f (3) breaking and theU A (1) anomaly

We extend our previous investigation about the flavor mixing or the OZI violating process in the light quark systems with the use of the generalized Nambu-Jona-Lasinio model incorporating theU _A (1) anomaly. The OZI breaking effects newly studied in the meson sector include the and meson decay constants, their couplings with nucleon as well as the masses and the mixing property of the scalar mesons. As for the baryon sector, we reexamine the strangeness content of the proton and the -N sigma term _N by taking into account the interactions between the constituent quarks. It is found that the short-range spin-spin interaction between the quarks gives anO(10 MeV)-enhancement for the theoretical value of the sigma term. Anomalous quark contents of other octet and decuplet baryons (hyperons) are also examined. It is shown that the axial anomaly induces the anomalous quark contents which are not expected in the naive quark model, while the short-range interaction between the quarks acts to suppress (enhance) the quark contents of the decuplet (octet) baryons. All the results indicate that the following picture holds systematically:m _s is so large that (i) the strangeness mixing induced by the anomaly is considerably suppressed and that (ii) the naive chiral perturbation does not work in the strange sector even in the tree level of the meson fields (largeN _c limit). The spin problem of nucleon, which is another subject related to the flavor mixing, is also examined with the use of our effective model.This paper is a modified version of the paper SUNY-NTG-89-49, RYU-THP-89-2 (August 1989)     

Dynamical Model of QCD Vacuum and Quark Confinement

The phase transition of a simple local gauge model is investigated in termsof the Nambu-Jona-Lasinio mechanism and it is pointed out that thephysical vacuum of QCD is bound state of quark-antiquark pairs which can beviewed, generally, as a nearly perfect color dia-electric medium. Animportant relation between the vacuum expectation value of gauge fields andscalar fields is also derived by solving the Euler equation for the gaugefields. Based on this relation the SU_C(3) gauge potential is given which can be used to explain the asymptotic behavior and confinement of quarks in a hadron, and at the same time the Yukawa potential of strong interaction can be given too.     

An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.     

On the hadronic problem in QCD

In this talk we try to give a brief review of the current ideas about confinement and the hadron problem in quantum chromodynamics.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.I would like to thank Rod Crewther, Peter Minkowski, William Mecklenburg, Werner Nahm, Jan Stern and John Strathdee for discussions which helped clarify many points in preparing this paper.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.