Vector SO(3) gauged O(4) sigma models on R 3 are presented. The topological charge supplying the lower bound on the energy and rendering the soliton stable coincides with the Baryon number of the Skyrmion. These solitons have vanishing magnetic monopole flux. To exhibit the existence of such solitons, the equations of motion of one of these models is integrated numerically. The structure of the...

In this paper, we study the nonlinear eigenvalue field equation −∆u+ V (|x|)u+ ε(−∆pu+W ′(u)) = μu where u is a function from Rn to Rn+1 with n ≥ 3, ε is a positive parameter and p > n. We find a multiplicity of solutions, symmetric with respect to an action of the orthogonal group O(n): For any q ∈ Z we prove the existence of finitely many pairs (u, μ) solutions for ε sufficiently small, where...

We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective σ-models and allows to formulate the topological charge density entirely in terms of σ-model fields. The method is studied in details and for thermalized vacuum configurations is shown to be compatible with overlap-based definition. We co...

Two-dimensional conformally parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP N−1 sigma model. The Lie-point symmetries of the CP N−1 model are computed for arbitrary N . The Weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed. Thi...

where e, e label the helicity states and k is the momentum transfer. In a naive wave function picture G1(0) can be interpreted as the fraction of the nucleon spin carried by the quarks. Experimental determinations lead to an unexpectedly small value of G1(0), calling for a theoretical explanation in the context of a nonperturbative study in QCD. G1(0) can be extracted from the nucleon matrix el...

The conditions leading to a nontrivial renormalization of the topological charge in four–dimensional Yang–Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological interaction, quantum effects due to the gauge bosons lead to a finite multiplicative renormalization of the θ–parameter while fermions give rise to an additional shift o...

In a somewhat overlooked work by Seiberg, a definition of the topological charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and Lüschers charge definition are related up to the section of the bundle. With the continued interest in baryon number violating processes, Seibergs paper is useful since it allows for a Chern-Simons number also.

The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2(Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investiga...

We show that, if the formula for the topological charge density operator suggested by fermions obeying the Ginsparg–Wilson relation is employed, it is possible to give a precise and unambiguous definition of the topological susceptibility in full QCD, χ full tL , for finite quark masses on the lattice. The lattice expression of χ full tL looks like the formal continuum one, in the sense that no...

We present preliminary results for the topological charge and susceptibility determined from the low-lying eigenmodes of the Wilson-Dirac operator. These modes have been computed on dynamical configurations with N f = 2 non-perturbatively improved Wilson fermions. We compare our results with the eigenmodes of fermions in the quenched approximation.