Nucleon scattering by the classical gravitational field is described by the gravitational (energymomentum tensor) form factors (GFFs), which also control the partition of nucleon spin between the total angular momenta of quarks and gluons. The equivalence principle (EP) for spin dynamics results in the identically zero anomalous gravitomagnetic moment, which is the straightforward analog of its electromagnetic counterpart. The extended EP (ExEP) describes its (approximate) validity separately for quarks and gluons and, in turn, results in equal partition of the momentum and total angular momentum. It is violated in quantum electrodynamics and perturbative quantum chromodynamics (QCD), but may be restored in nonperturbative QCD because of confinement and spontaneous chiral symmetry breaking, which is supported by models and lattice QCD calculations. It may, in principle, be checked by extracting the generalized parton distributions from hard exclusive processes. The EP for spin-1 hadrons is also manifested in inclusive processes (deep inelastic scattering and the Drell–Yan process) in sum rules for tensor structure functions and parton distributions. The ExEP may originate in either gravity-proof confinement or in the closeness of the GFF to its asymptotic values in relation to the mediocrity principle. The GFFs in time-like regions reveal some similarity between inflation and annihilation.

By comparing the cross sections for left- and right-handed electrons scattered from various unpolarized nuclear targets, the small parity-violating asymmetry can be measured. These asymmetry data probe a wide variety of important topics, including searches for new fundamental interactions and important features of nuclear structure that cannot be studied with other probes. A special feature of these experiments is that the results are interpreted with remarkably few theoretical uncertainties, which justifies pushing the experiments to the highest possible precision. To measure the small asymmetries accurately, a number of novel experimental techniques have been developed.

This article presents a review of our present understanding of the spin structure of the unpolarized hadron. Particular attention is paid to the quark sector at leading twist, namely, the quark Boer–Mulders function, which describes the transverse polarization of the quark inside an unpolarized hadron. After introducing the operator definition of the Boer–Mulders function, a detailed treatment of different non-perturbative calculations of the Boer–Mulders functions is provided. The phenomenology in Drell–Yan processes and semi-inclusive leptoproduction, including the extraction of the quark and antiquark Boer–Mulders functions from experimental data, is presented comprehensively. Finally, prospects for future theoretical studies and experimental measurements are presented in brief.

We present a short overview of studies of the transverse-momentum-dependent parton distribution functions of the nucleon. The aim of such studies is to provide three-dimensional imaging of the nucleon and a comprehensive description of semi-inclusive high-energy reactions. By summarizing what we have done in constructing the theoretical framework for inclusive deep inelastic lepton–nucleon scattering and one-dimensional imaging of the nucleon, we try to sketch out an outline of what we need to do to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three-dimensional gauge-invariant parton distributions. Next, we present an overview of what we have alr ady achieved, with an emphasis on the theoretical framework for semi-inclusive reactions in leading-order perturbative quantum chromodynamics but with leading and higher twist contributions. We summarize in particular the results for the differential cross section and azimuthal spin asymmetries in terms of the gauge-invariant transverse-momentum-dependent parton distribution functions. We also briefly summarize the available experimental results on semi-inclusive reactions and the parameterizations of transverse-momentum-dependent parton distributions extracted from them and present an outlook for future studies.

Both the PHENIX and STAR experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory are running polarized proton–proton collisions at s= 200 and 500 GeV. The main goal of the RHIC spin physics program is to gain deeper insight into the spin structure of the nucleon. We will give an overview of recent spin results from RHIC, particularly the study of gluon polarization via jet/hadron production and sea quark polarization via W boson production in longitudinally polarized proton–proton collisions.

It is well known that noncentral nuclear forces, such as the spin–orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known because only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may convey useful information about the in-medium properties of noncentral nuclear interactions, besides earlier studies using the time-dependent Hartree–Fock approach to understand the effects of spin–orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore the dynamical effects of noncentral nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focus of these studies has been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies but so far there are still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.