Dynamical resolution of theU (1) problem in QCD

The nonperturbative and perturbative aspects of theU(1) problem are discussed and linked to the dynamical breakdown of chiral symmetry in QCD. Then aU(1) gap equation is obtained and is approximately saturated with two-gluon intermediate states corresponding to theU(1) anomaly and consistent with η?η′ mixing.     

Dirac equation in Robertson-Walker metric

We recast the Dirac relativistic equation within the theoretical framework of the Robertson-Walker metric, using spatial hypersurfaces that are essentially curved, and hence more general, as compared to the flat ones employed by Barut and Duru.     

SL(n+1, C) strata and orbits in the solution space of Euclidean CP n models

We further study the action of SL(n+1, C) on the space of finite action solutions of the bidimensional Euclidean CP ⁿ models. We decompose the space of k-instantons into strata. Each stratum in characterized by an integer m with 0mmin(k, n) which can be calculated from the instanton by purely algebraic means. The k-instantons with m=n are called generic. Their stratum is shown to be dense in the space of k-instantons when kn. The isotropy subgroups for each stratum are identified.

---

Résumé Nous poursuivons l'étude de l'action de SL(n+1, C) sur l'espace des solutions à action finie du modèle CP ⁿ sur l'espace euclidien bi-dimensionnel. L'espace des k-instantons est décomposé en strates. Chaque strate est caractérisée par un entier m tel que 0 mmin(k, n) et qui peut être calculé à partir de l'instanton par des méthodes purement algébriques. Les k-instantons avec m=n sont dits génériques. Leur strate est dense dans l'espace des k-instantons (lorsque k n). Les sous-groupes d'isotropie de chacune des strates sont identifiés.

---

---

Supported in part by the Natural Sciences and Engineering Research Council of Canada and by the Fonds FCAR pour l'aide et le soutien à la recherche.     

On CP 1 and CP 2 Maps and Weierstrass Representations for Surfaces Immersed into Multi-Dimensional Euclidean Spaces

Abstract

An extension of the classic Enneper–Weierstrass representation for conformally parametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP ¹ and CP ² sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and 8-dimensional spaces, respectively. Relations of Weierstrass type systems to the equations of these sigma models are established. In particular, it is demonstrated that the generalised Weierstrass representation can admit different CMC-surfaces in ?³ which have globally the same Gauss map. A new procedure for constructing CMC-surfaces in ?ⁿ is presented and illustrated in some explicit examples.     

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.     

Colored monopole and strong CP

A systematic application of the collective coordinate method to quantization of spontaneously broken gauge theories with fermions, such as GUTs, in the monopole sector is presented. Usual and unusual charge properties of the ground state GUT monopole induced by CP violation, and in particular by the fact that θ_QCD ≠ θ_EM, are studied. In the presence of axions, semiclassically the ground state of GUT monopole is an actual realization of a spherical color-capacitor with the capacitance controlled by the magnitude of the Peccei-Quinn symmetry breaking scale. The “vacuum” around it is characterized by strongly enhanced (strong) CP violation and extends considerably far outside the monopole core. The effect of light fermions is studied in some detail. The possibility that even in the presence of axions (i.e. θ_QCD=0) there might be a non-vanishing and, in general, order-one color electric charge on the monopole ground state is pointed out.     

A solution to the strong CP problem in the SU(5) model

The possibility of naturally suppressing strong CP violation in the grand unified SU(5) model is examined. We show that a recent solution to the quark-lepton mass ratio problem by Georgi and Jarlskog can be extended in such a way as to yield a zero strong CP-violating parameter θ at the tree level and a small value for it coming from higher-order effects, along with reasonable mass ratios and mixing angles. Several phenomenological implications of the model are noted.     

Dirac equation in (1+1)-dimensional curved space-time

The Dirac equation in (1+1)-dimensional curved space-time is solved explicitly for the spatially flat Robertson-Walker space-time and the cigar metric considered by Witten.     

Dirac Operator on Fuzzy Sphere with U（1） Dirac Monopole Background

We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.     

Dirac Operator on Fuzzy Sphere with U(1) Dirac Monopole Background

We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.     

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)     

Majorana mass of the electron-muon Dirac neutrino and the fermion masses

The left-handed electron and muon neutrinos are considered to be Majorana neutrinos with equal mass. They have oppositeCP parities and are equivalent to a single Dirac neutrino. These neutrinos are shown to have a Majorana mass of about 6.5 eV. The relatively large mass of their charged leptons is due to their γ₅ coupling with the Higgs scalars By expressing the Higgs scalars as Clebsch-Gordon type of combinations ofZ andD neutral vector bosons with appropriate quantum numbers, it is shown that 2m _e m _μ /(m _e ² +m _μ ² )=(g_{v/g A}) _eμ ² , whereg _v andg _A are the vector and axial vector coupling constants, respectively, ofZ (orD) with the leptonse and μ. Weinberg mixing parametersx _L =e²/g _L ² andx _R =e ²/g _R ² are determined to be 0.2254 and 0.2746, respectively. In the quark sector the Cabibbo angle is about 13°11′ and the masses oft andb quarks are found to be respectively 134.2 and 4.69 GeV.     

The fermion vacuum in the (1+1)-dimensional chiral bag

The fermionic vacuum of the (1+1)-dimensional chiral bag of Zahed is examined in a time-dependent, adiabatic approximation. It is shown that the adiabatic vacuum gives rise to an oscillating boson field at the bag surface, whose excitation energies are in the same range as those of the valence quarks.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.