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We investigate the consequences of assuming that there is an observable axial-vector current ${J}_{5\ensuremath{\mu}}$ in theories of finite quantum electrodynamics (QED). Positivity constraints for the matrix elements of ${J}_{5\ensuremath{\mu}}$ can be neatly formulated for the massive theory via the Schwarz inequality. In order that these requirements be satisfied in the presence of a nonvanishing anomalous constant $S$, it is essential that $d$, the dimension of ${J}_{5\ensuremath{\mu}}$, be greater than 3. In that case, we can explain why the condition ${J}_{\ensuremath{\mu}}|0〉=0$ satisfied by the electromagnetic current ${J}_{\ensuremath{\mu}}$ in the zero-mass theory does not contradict the Adler-Bardeen theorem ($S\ensuremath{\ne}\mathrm{O}$). Further, we explain why the photon-photon scattering subgraphs which cause the anomaly in $d$ are not asymptotically negligible in the Johnson-Baker-Willey (JBW) and Adler versions of finite QED: The argument for $d=3$ fails because it involves the use of an illegal skeleton expansion. The value of $d$ depends on the number of fundamental fermion species in the theory. Vector and axial-vector currents which generate a non-Abelian internal symmetry of the fermions cannot be introduced in the JBW and Adler theories, because the relevant positivity conditions cannot be satisfied. We examine evidence that the infinite perturbative sums are sufficiently irregular to permit this situation. In an appendix, we solve the Callan-Symanzik equations in the asymptotic region when the zero ${\ensuremath{\alpha}}_{e}$ of the Callan-Symanzik function $\ensuremath{\beta}(\ensuremath{\alpha})$ is not simple. In general, violations of asymptotic scale invariance occur if the physical coupling constant is not equal to ${\ensuremath{\alpha}}_{e}$. In the JBW model, this phenomenon can be readily interpreted diagrammatically for matrix elements of ${J}_{5\ensuremath{\mu}}$ and the electron propagator.

General connections between exclusive and inclusive cross sections are studied by the generating-functional technique. Exclusive cross sections, inclusive cross sections, and correlation functions appear as coefficients of different Taylor series expansions of the same generating functional. Also studied are the connections between semi-inclusive processes where all charged particles in an event are observed and genuine inclusive processes with only some of the charged particles observed. No information on neutral particles enter in these connections for semi-inclusive processes. In special cases our results reproduce several seemingly unrelated aspects of inclusive processes treated by Mueller, Predazzi, and Veneziano and by Campbell and Chang. Our approach yields additional constraints and sum rules for inclusive cross sections. It is established that an infinite number of correlation functions are needed; and correlation in the pionization region necessarily exists if the multiplicity increases with energy and the transverse momenta of the final particles are limited. A brief comparison between exclusive and inclusive cluster decomposition is given. The question of diffraction dissociation is also very briefly discussed.

We combine chiral and "scaling" Ward identities in an analysis of the axial-vector current anomaly. This leads to a proof of the Adler-Bardeen theorem. The "scaling" Ward identities we used may be properly called "response equations"; they are slight generalizations of the Callan-Symanzik equation. Our discussion is given for a class of theories which includes the $\ensuremath{\sigma}$ model and massive vector-boson theory.

We use Wilson's theory of broken scale invariance to study the anomaly of axial-vector current in a world with one space and one time dimension. It is shown that in the Schwinger and Thirring models, Wilson's approach and the perturbative approach yield similar results for the anomaly of partial conservation of axial-vector current.

Inclusive measurement of hadron collisions has recent ly in teres ted bo th exper imentalists and theorists . Al though not enough expe r imen ta l da t a have been accumulated , the problem has been inves t iga ted f rom var ious theore t ica l v iewpoints , such as pa r ton model, mul t iper iphera l model, l imi t ingf ragmenta t ion t heo ry and phenomenological 02,1 expansion. In this le t ter we present another theore t ica l approach to inclusive processes th rough current algebras. To be specific let us consider an equal t ime c o m m u t a t o r

We discuss the $s$-channel unitarity constraint of the multiperipheral bootstrap models. We show that, if the low-subenergy part of the kernel is weak, it is possible to have self-consistent Regge poles. On the other hand, if the low-subenergy part of the kernel is strong, we can never have self-consistent Regge poles. In this case the most important $J$-plane singularity is a cut with branch point at 1, and the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering amplitude goes to infinity slower than $\frac{s}{\mathrm{ln}s}$ at high energy.

The Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model is modified to study deep-inelastic electron-nucleon scattering. The behavior of the structure functions is derived in the limit of large energy and momentum transfer, $\ensuremath{\nu}$ and ${q}^{2}$, with $\ensuremath{\omega}\ensuremath{\equiv}\frac{2m\ensuremath{\nu}}{(\ensuremath{-}{q}^{2})}$ fixed but large. In particular, scaling is derived. To accomplish this derivation it is necessary to introduce a cutoff for the momentum transfer of the exchange nucleon, which directly couples to the photon in the multiperipheral chain. The multiperipheral derivation is compared with derivations that use other models. The generality of our derivation, in the sense of requiring only Regge behavior and a particular asymptotic off-shell dependence, is discussed.

An exactly soluble model of the renormalization group for two-dimensional quantum electrodynamics is presented. The theory has a nontrivial eigenvalue at which it is scale-invariant and some operators acquire anomalous dimensions. Finally, the anomalous constant associated with the axial-vector current is independent of the coupling constant away from the eigenvalue, but vanishes at the eigenvalue.

In finite theories of quantum electrodynamics, positivity implies d> 3 for the dimension d of an axial-vector current J/sub 5 mu / with nonzero anomaly. This result is not contradicted in the Johnson-Baker-Willey and Adler models: Arguments for the neglect of intenal fermion creation and annihilation fail for J/ sub 5 mu / amplitudes because illegal skelet on expansions are involved.

The ordering of the alloy AgAuZn2 has been studied by means of X-ray diffracto-metry. The specimens were quenched from 600℃ and subsequently annealed at 100℃ for various periods of time. It was shown that in the quenched condition almost all of the Zn atoms were at their appropriate lattice sites, whereas the Ag and Au atoms were comparatively less readily to occupy their right places. A very short period of annealing at 100?? was sufficient to make all the Zn atoms take their proper positions. The ordering among Ag and Au atoms proceeded as annealing was continued, the positions of Zn atoms being unaffected. The size of antiphase domains deduced depended markedly on the indices of reflections during the early stage of domain growth. The final sizes attained in different directions, however, were practically the same. The ordering of atoms and the growth of domains took place simultaneously. However, the degree of order reached a steady value long before the domains attained the final size.