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The Regge contribution to the six-particle amplitude is studied by going to five dimensions and considering a generalization of the usual helicity approach This has the advantages that the Steinmann relations are satisfied in a natural way, and that there are no spurious poles. The resulting representation can also be used to study more general limits than the usual multi-Regge limit. In particular, limits relevant to the two-particle inclusive cross section can be studied. The constraints imposed on this representation by Regge factorization are also considered.

The critical scattering parameters have been calculated for an Ising-like system in a field, below and above ${T}_{c}$ up to second order in $\ensuremath{\epsilon}(=4\ensuremath{-}d)$. The corrections to the Ornstein-Zernike form in the small- and large-$q\ensuremath{\xi}$ limit are presented and their relevance to experiments is discussed.

We investigate the conditions necessary for the existence of scattering solutions to the Bethe-Salpeter equation. We work with the causal Green's function in both timelike and spacelike regions of $x\ensuremath{-}{x}^{\ensuremath{'}}$. Our results indicate that high-momentum or small-relative-time limits must be taken. In the small-relative-time limit, suitable restrictions on the interaction $I(x)$ must also be considered.

>The techniques of Mueller analysis are applied to deep-inelastic processes such as e/sup -/p yields e/sup -/hX and nu p yields mu /sup -/hX, where h is a specified hadron and X is unobserved. In the combined Bjorken-Regge limit { omega = (2M nu /Q/sup 2/) fixed and large} there are three domains: the target fragmentation region, the central plateau, and the current-fragmentation region. Only the current-fragmentation region provides information not accessible in hadronic collisions. For this region we find an essentially unique Mueller description consistcnt with assumed Bjorken scaling for inclusive processes. A conclusion of the analyses is that the egments including a The Mueller description is compared with parton, multiperipheral, and other models. (auth)

It is shown rigorously that the introduction of random-hopping elements into an impurity potential in a material with a single band does not introduce any of the new phase shifts required to generally satisfy the Friedel sum rule in the dilute limit. With this proof it is now clear that the parameters required to satisfy the Friedel sum rule as suggested by Schwartz, Krakauer, and Fukuyama (SKF) are artificial in spite of the off-diagonal character of their model. Other models are suggested which give rise to phase shifts of more than one character. Also, it is demonstrated that the locator theory of Blackman, Esterling, and Berk (and hence that of Shiba) is a correct $s$-wave theory in the dilute limit in contrast to the claim of SKF.

Recent data on the π- / π + ratio for photoproduction in the first resonance region are analyzed using a model developed previously. Within the model, the data set an upper limit of about 3 percent on the ratio of isotensor to isovector resonance excitation, assuming T invariance. The pi radiative-capture data are investigated again within the model, to assess the evidence for this latter assumption.

Ab initio calculations for the multistate ket associated with the pair of molecular states arising from thc lowest-lying separated-atom limit are carried out. Comparison with the usual variational approach is made. Computational advantages, including the avoidance of multicenter exchange integrals, are discussed. (auth)

With the aid of a general algorithm for expanding a given Heisenberg operator product in terms of $n$-particle irreducible operator products integrated over $c$-number Bethe-Salpeter kernels, we discuss the expansion of bilocal products near the light cone. It is shown that, to any finite order in perturbation theory, only a small number of terms in the operator-product expansion can be singular on the light cone. In particular, some of the bilocal operators which determine the scaling properties of deep-inelastic electroproduction have potential singularities determined by operator-valued Bethe-Salpeter equations involving only these bilocals themselves (plus local fields). A generalization of the light-cone Bjorken-Johnson-Low (BJL) limit is given which reveals logarithmic singularities which occur in $T$ products but not in commutators; this BJL limit is applied systematically to Feynman graphs in another paper. As a special case, the Wilson expansion is recovered.

The transition-operator boson introduced by Dreizler and Klein has been analyzed in detail, and the exact expression for angular momentum operators in terms of the boson has been obtained. The method is found to be applicable only in the asymptotic limit of the large nuclear number. Its relation to another representation due to Holstein and Primakoff has also been investigated.

For an infinite linear chain the authors consider the atomic limit of an extended Hubbard model which takes into account the nearest neighbor interatomic electron-electro repulsion. The specific heat, static magnetic susceptibility, and density-density correlation function are studied exactly at any temperature for the half-filled band case. The authors discuss also the quarter-filled band in the limit of infinite intra-atomic Coulomb repulsion. (Author)

A correlated-effective-field theory is defined for interacting oscillators each moving in a local potential well of arbitrary form. Correlations are introduced into an effective-field framework and determined by forcing a consistency with the fluctuation theorem. The theory is formulated for both ordered and disordered phases as a model for a structural phase transition. In the limit of a quasiharmonic local potential the linearized theory is shown to be formally equivalent to self-consistent phonon theory for classical motion. In an opposite limit of extreme anharmonicity, with a deep-double-well local potential, the method is compared to Ising theory and shown to be equivalent to the spherical approximation.

A hard-pion model is presented for a general symmetry. In the case of strong partially conserved currents the proper vertices are assumed to be analytical. Ward-like identities are obtained for the contact terms. For the soft-pion process in the symrnetry limit of SU(2) x SU(2) a phenomenological Lagrangian is built, which reproduces the results of the hard-pion model. As an illustration we deal with the K/sub 13/ problem, and build an amplitude for the photoproduction process gamma N yields pi N. (auth)

The equilibrium properties of a model ferroelectric have been investigated in classical approximation. For the displacive limit and $Tl{T}_{c}$ strong indications are given that even for short-range interaction the self-consistent-phonon mean-field approximation describes the exact temperature behavior outside a region $\frac{|T\ensuremath{-}{T}_{c}|}{{T}_{c}}$ which tends to zero in the very displacive limit. In the order-disorder limit, high-and low-temperature expansions as well as a comparison of free energies show that a Curie-Weiss (independent-site) mean-field approximation, though not being exact, is to be preferred over a self-consistent-phonon approach.

The physical origins and dynamical details of Regge behavior are studied by examining a general class of theories which are capable of describing the observed large-momentum-transfer data and extending them into the intermediate-t range. The mechanism responsible for the smooth connection between the deep-scattering region and the Regge region is discussed in detail. We derive a convenient new form of the exact integral equation which describes generalized ladder graphs containing irreducible scattering amplitudes as the rungs. The limiting behavior of the Regge trajectories and residues are then calculated in both the single-channel and the more realistic coupled-channel cases. The trajectories are found to approach negative constants for large negative momentum transfer and the residues fall as powers in the same limit. Furthermore, since the forward and backward Regge regimes must join smoothly onto the same fixed-angle behavior, there are relations between a priori unrelated trajectory functions and residues. The standard properties of Regge poles, in particular factorization and signature, are shown to be present even though the basic, fixed-angle interaction possesses neither of these properties. These general considerations are then applied to the more specific constituent-interchange model. Here we find that the asymptotic behavior of the trajectories and residues are controlled by the form factors of the particles involved in the scattering. Finally, we elucidate the relationship between the constituent-interchange diagrams and the Harari-Rosner duality diagrams.

The concept of scaling dimensions is important in the physics of large systems, in particular, in the statistical mechanics of critical phenomena. The main purpose of this article is to explain and formulate this important concept in a more transparent and precise fashion. Discussion is in the framework of the $n$-component classical spin model and the renormalization group. It is emphasized that not every quantity, but only special ones, called scaling variables, have well-defined scaling dimensions. In general these variables can be derived by making use of certain parameters which are the scaling fields of Wegner. The dimensions are simply related to the exponents associated with the renormalization group. We hope to extract a fairly concrete picture by a general formulation followed by explicit determination of the scaling variables in the large-$n$ limit. Dimensions are obtained to $O(\frac{1}{n})$.

Dipole electric transitions with $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}1$ are studied theoretically for odd-mass nuclei in the rare-earth region (i) in the frame work of an elaborated Nilsson model with rotation-particle coupling and with isospin-dependent parameters, (ii) with the usual BCS wave function, and (iii) with sharp particle-number-projected BCS wave functions. These projected wave functions are the limit of very speedily converging sequences of functions. General formulas for the pairing reduction factors with strict nucleon number conservation are established. The unphysical effects due to particle fluctuation in the usual BCS wave functions are found to be very important in the theoretical BCS evaluation of reduction factors and half-lives. In most of the analyzed $E1$ transitions, the hindrance factors are improved by the elimination of the unphysical effects due to particle fluctuation. The blocking effect is systematically taken into account. The importance and validity of the physical and mathematical approximations used is discussed.

Two-variable Galilei-group expansions are derived for the two-particle nonrelativistic scattering amplitude. These expansions contain the usual partial-wave and eikonal expansions and supplement them by further expansions in the remaining kinematic variable. The expansions are written both for square-integrable and for asymptotically increasing amplitudes and are shown to correspond to the nonrelativistic limit of previously considered relativistic two-variable expansions. Dynamical singularities (Breit-Wigner resonances, bound states, poles in the impact-parameter plane, etc.) are investigated and related to the asymptotic behavior of the expansion coefficients (or Galilei amplitudes). The threshold and high-energy limits of the expansions are discussed. As a mathematical by-product we give a classification of the subgroups of E(3) and also some results on the representation theory of this group; in particular we study the Clebsch-Gordan coefficients.

The Glauber version of the eikonal expansion in potential theory is shown to be the unique result of calculating the high-energy, fixed-momentum-transfer limit of the Born series. Correction terms are systematically calculated and agree with the form proposed by Wallace. These results are used to understand the fact that the Glauber eikonal is an accurate approximation to the exact scattering amplitude at all energies.

The structure of the Neveu-Schwarz model in multi-Regge limits is studied, with particular emphasis on quantum-number effects on Reggeon-particle vertex functions.

We study the thermoelectric power of a narrow-band Hubbard chain with an arbitrary number of electrons per site. The calculations are carried out to the lowest order in the transfer integral. We find a characteristic electron density ($\ensuremath{\rho}=\frac{2}{3}$) below which the thermoelectric power is negative at all temperatures. In contrast, for $\ensuremath{\rho}g\frac{2}{3}$, the thermoelectric power is small and negative only above a characteristic temperature, below which there is a change of sign and slope. We comment on the applicability of these results to the charge-transfer salts of tetracyanoquinodimethan (TCNQ).

The solution of the isotropic $n$-component spin models by expanding in powers of $\frac{1}{n}$ has been very helpful in studying static critical phenomena. The limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$ is the spherical model. There are many possible generalizations of these models for studying dynamic (time dependent) critical phenomena. In this paper we study the propagation of sound waves and heat diffusion near the critical point in a $\frac{n}{2}$- component complex-spin (each complex component has two real components) model in the limit of large $n$. This model is a particular dynamic generalization of the spherical model and is equivalent to a system of bosons obeying quantum mechanics.

We offer clarifications and connections to thc Atwood-West method of extracting neutron cross sections from deuterium data. Another expression for the flux factor is derived. Also, an inconsistency in the electroproduction expressions in the qi = 0 limit is discussed, and possible solutions are mentioned. (auth)

The sixth frequency moment of the spectral functions of both the longitudinal and transverse current correlations along with their self-parts has been derived for a system of particles interacting through a two-body potential. The first two frequency moments of the spectral function of the energy-density fluctuation, and the first four frequency moments of the spectral function of the kinetic-energy-density fluctuation-correlation functions have also been derived. Numerical estimates for the fourth and sixth frequency moments of the spectral function of the longitudinal current correlations have been made for liquid argon. From this some information about the behavior of the contributions of triplet and quadruplet correlation functions to the frequency moments of liquid argon have been obtained. Numerical estimates have also been made for the first four frequency moments of the kinetic-energy-density fluctuation-correlation function in the long-wavelength limit for liquid argon.

We discuss a theory of $\mathrm{CP}$ noninvariance in which the interaction is completely determined by the principle of gauge invariance. We also discuss its experimental test by observing anomalous phenomena of ${K}^{0}$ decay in the electric field. Moreover, the experimental result can also determine an accurate upper limit for the neutral kaon charge (which has never been directly measured) if the predicted phenomena are not observed.

A unified account for the isovector contribution to $\ensuremath{\rho}$ production, pion photoproduction, and electroproduction in the near-forward direction of the pion is given, and its relationship to vector-meson dominance is discussed. The high-energy limit is discussed in detail, first for the electric Born model, and then for a more realistic model derived from fixed-$t$ dispersion relations. Very simple features emerge, which in most cases can also be observed at low energies. Numerical results of our model are given for all three types of reactions.

The limit ${Z}_{3}=0$ is studied in the Zachariasen model using dispersion theory techniques. The connection between bound states and elementary particles is demonstrated in this limit and it is shown how Castillejo-Dalitz-Dyson ambiguities are removed.

The calculation of the partftion function for a simple onedimensional order-disorder model is reduced to the solution of a certain functional equation. This equation is rigorously and it is shown that in the limit of indefinitely long-range interactions the model exhibits a finite discontinuity in the specific heat. (auth)

It is shown that the ensemble-averaged single-particle Green's function for an electron in a disordered $n$-component alloy is described by a simple expression in the coherent-potential approximation. Within the appropriate limits, it exhibits dilute alloy, virtual crystal, weak-coupling limit, and atomic behaviors. For a special model band structure of parabolic form, the problem of evaluating the quasiparticle density of states is reduced to that of solving a polynomial of $n+1$ order, which has either $n+1$ real solutions or $n\ensuremath{-}1$ real solutions in addition to two complex-conjugate solutions for a given set of parameters. The types of the density of states \char22{} persistence or amalgamation \char22{} are judged by the types of solutions. The formulation is also useful to prove the sum rules for the numbers of states. In the limit of $n$ infinite, continuous distributions of atomic levels are studied and the criterion for the Anderson transition is estimated.

An analysis of the recently measured photon-proton total cross sections is performed. Smooth fits to the cross sections are obtained and used to calculate, by means of the forward dispersion relation, the real part of the spin-averaged forward amplitude. The resulting predictions for the real part are given. At high energies, the fits to the present total cross-section data, together with the calculated real part, suggest the presence in the high-energy behavoir of an extra real constant in addition to what one would have predicted from Regge theory and the high-energy behavior of the imaginary part. This extra real constant, which is consistent in sign and magnitude with the Thomson limit, −αMN, could correspond to a fixed pole at J=0 in Regge-pole language. Possible ways to test the forward dispersion relation are discussed.

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The hadron is considered to be a compound with two or more constituents circulating freely in a box of radius ≈10^-13 cm. The density of hadron levels, ρ (m), is estimated from the number of states in the box (statistical condition) and is also required to be consistent with the spectrum of constituents, which are assumed to be the hadrons themselves (bootstrap condition). This type of model was first considered by Hagedorn, who obtained a solution of form ρ m∼cm^ae^(bm) with a=-5/2 which satisfied the bootstrap condition asymptotically to within a power of m. We obtain a solution with a

Precise measurements of the critical field of superconducting tin films were made as a function of temperature and thickness. Particular attention was paid to measurements near the transition temperature where the London limit holds. It was found that near the transition temperature the critical field could be expressed in the form ${H}_{c}={(\ensuremath{\Delta}t)}^{\frac{1}{2}}\ensuremath{\gamma}(1+\ensuremath{\epsilon}\ensuremath{\Delta}t)$, where $\ensuremath{\gamma}$ and $\ensuremath{\epsilon}$ are independent of temperature. In terms of the Ginzburg-Landau theory modified to include the lower temperatures, the constant $\ensuremath{\gamma}$ determines the penetration depth and the constant $\ensuremath{\epsilon}$ is different for different modifications of the field-independent free energy.Penetration depths determined in this way were found to be a function of thickness. Assuming that the coherence length $\ensuremath{\xi}$ in the film is determined by the thickness and using the expression for the thickness dependence of the penetration depth given by Tinkham, one can obtain a bulk coherence length ${\ensuremath{\xi}}_{0}$ of approximately 2100 \AA{}, as well as a bulk penetration depth of 510 \AA{}, from the data. This way of determining ${\ensuremath{\xi}}_{0}$ is quite different from the high-frequency method of Pippard, and it is proposed as an independent and alternative method.Two particular modifications of the Ginzburg-Landau theory are considered. The first, which is the original theory, predicts a value of $\ensuremath{\epsilon}=0.31$. The second, which is the Gorter-Casimir modification proposed by Bardeen, predicts a value of $\ensuremath{\epsilon}=\ensuremath{-}0.19$. Experimentally, $\ensuremath{\epsilon}$ was determined to have an average value of 0.14\ifmmode\pm\else\textpm\fi{}0.10.

It is shown how to obtain consequences of current algebra for nonleptonic hyperon decays in the limit ${q}^{2}=0$, with the baryons kept on the mass shell. The $p$ waves are model-independent, and an excellent fit determines the parity-conserving spurion. When a ${K}^{*}$ pole is included for $s$ waves, a rough fit is achieved.

A relativistic pseudopotential is defined for the Dirac Hamiltonian with the use of relativistic orthogonalized plane waves. In the standard representation, the leading new terms in the Dirac pseudo-Hamiltonian are a mass-change term, a change in the timelike component of the vector potential, and spatial components of bivector and pseudovector contributions. The former two give rise to the "repulsive" part of the pseudopotential in the nonrelativistic limit. The latter are "rotational" energy contributions due to core overlap which give rise to the spinorbit corrections of the more usual treatments. The nature of the spin-orbit interaction is discussed in some detail.

We present a sum rule for the $\ensuremath{\Sigma}$ term derived from the assumptions of Bjorken limit, precocious asymptopia, and finite-mass dispersion relations. We use the commutation relations of the gluon model as input for a numerical evaluation.