Narrow Results

Measurements of double-spin asymmetries for single-inclusive heavy flavor production and for heavy quark correlations are expected to provide valuable information about the spin structure of the nucleon, in particular, the elusive gluon polarization. We discuss progress towards a versatile parton-level Monte-Carlo code for the production and decay of heavy quarks in longitudinally polarized hadron-hadron and photon-hadron collisions at next-to-leading order accuracy of QCD. Phenomenological studies are presented for BNL-RHIC and COMPASS.

Recent results on the study of the electromagnetic structure of nucleon resonances, the spin structure of protons and neutrons at small and intermediate photon virtuality, and the search for exotic pentaquark baryons are presented.

In this paper we calculate spin dependence of parton distributions and proton structure function. The polarized valon distributions in a proton and the polarized parton distributions inside the valon are necessary to obtain the polarized parton distributions in a proton. The results of our calculations for the proton structure function, are in good agreement with the available experimental data. We obtain the spin contribution and angular momentum of the valons to the proton.

I briefly review some of the interesting recent results on neutron spin structure that have been obtained using the Jefferson Lab Hall A facility with a polarized ³He target.

The spin physics with hadrons has entered the new era with the completion of the first polarized proton collider, RHIC at Brookhaven National Laboratory. The spin physics program at RHIC provides a unique opportunity to elucidate the spin structure of the nucleon and to investigate the symmetries embeded in the nature. First set of physics results from the program are described with near future prospects.

The quantum properties of localized finite energy solutions to classical Euler–Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant g is constructed, taking into account the conservation laws of momentum and angular momentum (invariance of the action with respect to the group of motion M(3) of three-dimensional Euclidean space) rigorously in every order of perturbation theory.

We show that the linking signature of a closed oriented 4-manifold with infinite cyclic first homology is twice the Rochlin invariant of an exact leaf with a spin support if such a leaf exists. In particular, the linking signature of a surface-knot in the 4-sphere is twice the Rochlin invariant of an exact leaf of an associated closed spin 4-manifold with infinite cyclic first homology. As an application, we characterize a difference between the spin structures on a homology quaternion space in terms of closed oriented 4-manifolds with infinite cyclic first homology, so that we can obtain examples showing that some different punctured embeddings into S⁴ produce different Rochlin invariants for some homology quaternion spaces.

We give the explicit formula of the spin-refined Reshetikhin–Turaev SU(2) invariants of lens spaces. Using this result, we also give the formula of the spin-refined Turaev–Viro SU(2) invariants of lens spaces.

We define the 2-signatures, 2-nullities and Arf invariants (when possible) for links which are null-homologous modulo two in a rational homology three-sphere. We define these invariants using the Goeritz form on non-oriented spanning surfaces. We develop their cobordism properties from this point of view. We give a good way to index these invariants. We also define d-signatures and d-nullities for links which are null-homologous modulo d in a rational homology sphere from the point of view of branched covers. We index d-signatures and d-nullities and develop their cobordism properties. Finally we define Arf invariants (when possible) in a general closed 3-manifold using spin structures.

It is known that the complex spin group Spin(n, ℂ) is the universal covering group of complex orthogonal group SO(n, ℂ). In this work we construct a new kind of spinors on some classes of Kahler–Norden manifolds. The structure group of such a Kahler–Norden manifold is SO(n, ℂ) and has a lifting to Spin(n, ℂ). We prove that the Levi-Civita connection on M is an SO(n, ℂ)-connection. By using the spinor representation of the group Spin(n, ℂ), we define the spinor bundle S on M. Then we define covariant derivative operator ∇ on S and study some properties of ∇. Lastly we define Dirac operator on S.

Let $F_g$ be the closed orientable surface of genus $g$. We address the problem to extend torsion elements of the mapping class group $\mathcal{ℳ}(F_g)$ over the 4-sphere $S^4$. Let $w_g$ be a torsion element of maximum order in $\mathcal{ℳ}(F_g)$. Results including:

(1) For each $g$, $w_g$ is periodically extendable over $S^4$ for some non-smooth embedding $e:F_g\to S^4$, and not periodically extendable over $S^4$ for any smooth embedding $e:F_g\to S^4$.

(2) For each $g$, $w_g$ is extendable over $S^4$ for some smooth embedding $e:F_g\to S^4$ if and only if $g=4k,4k+3$.

(3) Each torsion element of order $p$ in $\mathcal{ℳ}(F_g)$ is extendable over $S^4$ for some smooth embedding $e:F_g\to S^4$ if either (i) $p=3^m$ and $g$ is even; or (ii) $p=5^m$ and $g\ne 4k+2$; or (iii) $p=7^m$. Moreover, the conditions on $g$ in (i) and (ii) cannot be removed.