A review on the theoretical aspects and the experimental results of polarized deep inelastic scattering and of other hard scattering processes is presented. The longitudinally polarized structure functions are introduced and cross section fromulae are given for the case of photon as well as W ± and Z 0 exchange. Results from the SLAC and CERN polarization experiments are shown and compared with each other as well as their implications for the integrated g 1 (x, Q 2 ) are reviewed. More recent experiments presently underway (like HERMES at DESY) and future projects (like RHIC at BNL, HERA-N and a polarized HERA collider at DESY) are discussed too. The QCD interpretation and the LO and NLO Q 2 -evolution of g 1 , i.e. of the longitudinally polarized parton densities, is discussed in great detail, in particular the role of the polarized gluon density, as well as the expectations for x → 0. Particular emphasis is placed on the first moment of the polarized structure function in various factorization schemes, which is related to the axial anomaly, and on its relevance for understanding the origin of the proton spin. Sum rules (i.e. relations between moments of the structure functions) are derived and compared with recent experimental results. Various other phenomenological applications are discussed as well, in particular the parametrizations of polarized parton densities as obtained from recent data and their evolution in Q 2 . Furthermore, jet, heavy quark and direct photon production are reviewed as a sensitive probe of the polarized gluon density, and the physics prospects of the future polarized experiments at RHIC ( p p) and a polarized HERA collider ( e p) are studied. DIS semi-inclusive asymmetries and elastic neutrino-proton scattering are reviewed, which will help to disentangle the various polarized flavor densities in the nucleon. The status of single and double spin asymmetries, and the observation of handedness in the final state, are discussed as well. Structure 1 functions for higher spin hadrons and nuclei are defined and possible nuclear effects on high energy spin physics are reviewed. The theoretical concept of spin-dependent parton distributions and structure functions of the polarized photon is presented and possibilities for measuring them are briefly discussed. Various nonperturbative approaches to understand the origin of the proton spin are reviewed, such as the isosinglet U A (1) Goldberger-Treiman relation, lattice calculations and the chiral soliton model of the nucleon. The physical interpretation and model calculations of the transverse structure function g 2 are presented, as well as recent twist-3 measurements thereof, and the Burkhardt-Cottingham sum rule is revisited. Finally, the physics of chiral-odd 'transversity' distributions is described and experimental possibilities for delineating them are reviewed, which will be important for a complete understanding of the leading twist-2 sector of the nucleon's parton structure. In the Appendix the full 2-loop anomalous dimension...

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We consider the decay of a polarized top quark into a polarized W -boson plus a bottom quark, followed by the decay of the W -boson into a pair of leptons or quarks. The polar angle distribution of the top spin relative to the W -momentum and the polar angle distribution of the lepton (or quark) in the W -rest frame is governed by three polarized and three unpolarized rate functions which are related to the double density matrix elements of the decay t → W + + b. We obtain analytical expressions for the O(α s ) radiative corrections to the three polarized and three unpolarized rate functions. We also provide a comprehensive discussion of the dependence of the longitudinal, transverse and normal polarization of the top quarks produced at e + e − -colliders on beam polarization parameters.

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