International Journal of Modern Physics A

We review recent experimental data on polarization asymmetry at intermediate and high energies. We include phenomenological interpretations of the data.

In this review we examine the present status of polarization physics at intermediate and high energies. Special attention is directed to controversial experimental results as well as interpretations of the data. Our objective is to contribute toward the planning of future experimental facilities and experiments. For more detailed description and discussion of various experiments and phenomenological interpretations, we provide extensive references.

Polarized-beam programs at the SLC (Stanford Linear Collider), HERA (Hadron Electron Ring Accelerator, and EPC (Electron Positron Collider) are not included in this review. Neither do we discuss the technologies of polarized ion sources, polarized targets, polarized beams, or accelerators.

We have studied HERA's capability of precisely measuring various parameters of the electroweak standard model. The analysis was performed in kinematical regions, x≥0.01 and x≥0.1, where systematic errors are expected to be under control. The statistical precision reachable for standard model parameters, extracted from R≡σ_NC/σ_CC and NC asymmetries A for polarized e^± beams, was estimated for both regions. Heavy flavor contributions, which amount up to 15% to the cross sections, were included via the boson-gluon fusion process. Furthermore the influence of various uncertainties (parton distributions, quark masses, σ_L/σ_T fixing input parameters) was estimated. For x≥0.01 the uncertainties due to parton densities are sizeable, the total rates (cross sections), however, increase strongly in contrast to the region x≥0.1.

A critical analysis is given in order to set up a well-defined perturbative expansion for Yang-Mills Euclidean theories within the axial gauge choice, using Cauchy principal value prescription to handle the spurious singularities. It is shown that, following a mathematically meaningful and unambiguous procedure, the exponential behavior of the Euclidean Wilson loop does not occur at variance with the covariant and planar gauge choices. A comparison with previous similar approaches and results is worked out in order to clearly understand the reasons for the breakdown of gauge invariance in the present case. In particular we can conclude that the so far proposed alternative prescriptions, which have been claimed to restore gauge invariance, should be carefully reexamined, at least for the Euclidean formulation.

For a many-body relativistic fermionic system the concept of a hole state is useful. Consequently, the introduction of a field operator corresponding to these hole states is of technical convenience. We define the transformation that takes place from a particle to a hole and construct the corresponding hole-field-operator. Some physical consequences of pairing and possible condensation are explored. The advantage of the newly introduced hole-operator for symmetry considerations is shown.

We discuss the consistency (unitarity) of string propagation on the non-compact group SU(1,1)×G, and find the restriction on the level of the Kac-Moody algebra for this propagation to be unitary. We also suggest some modifications to the Virasoro generators and obtain a manifestly unitary string theory.

In this paper a topological construction of representations of the -series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle over the configuration space of η points in the complex plane. The fibres are homology spaces of configuration spaces of points in a punctured complex plane, with a suitable twisted local coefficient system, and there is thus a natural flat connection on the vector bundle. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, in which the monodromy of n-point functions for a conformal field theory on P¹ is used to produce a braid group representation which factors through the Hecke algebra.

A numerical approach to 2-D relativistic field theories is suggested. Considering a field theory model as an ultraviolet conformal field theory perturbed by a suitable relevant scalar operator one studies it in finite volume (on a circle). The perturbed Hamiltonian acts in the conformal field theory space of states and its matrix elements can be extracted from the conformal field theory. Truncation of the space at a reasonable level results in a finite dimensional problem for numerical analyses. The nonunitary field theory with the ultraviolet region controlled by the minimal conformal theory is studied in detail.

We present a method based on BRST techniques for how to obtain the conventional equations for symmetric tensor gauge fields which describe free massless particles of arbitrary integer spin. We do so in a wave function representation in a flat space-time background of any dimension. A fairly straightforward way is also presented for how to obtain the equations from a gauge invariant Lagrangian of the form .

We present a program based on BRST techniques for how to obtain the conventional equations for totally symmetric tensor-spinors which describe free massless particles of arbitrary half-integer spin. We do so in a wave function representation in a flat space-time background of any even dimension.