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The continuity of the phase shift and S ‐wave scattering length as a functional of the potential is considered. The question is investigated in the present article for sequences of square wells which converge pointwise to zero. The results show certain conditions to be sufficient for...
It is shown that each symmetry of a field theory with interaction and with a mass gap, induced by a local current, is also induced by at least two other currents, local with respect to the asymptotic free fields and bilinear in these fields. The currents are asymptotic currents in the sense of...
A new, and computationally simple, method is given for obtaining the characters of all the inequivalent irreducible vector representations of a finite group. The method was applied to determine the characters of the irreducible vector and ray representations of the four‐dimensional cubic...
Conditions are established under which the Dirac equation for an electron in an electromagnetic field has an exact semiclassical solution. In other words, the phase is identified with a solution of the corresponding relativistic Hamilton‐Jacobi equation and the spinor amplitude has no explicit...
The procedure of finding the states, which minimize the uncertainty product of two noncompatible observables, leads to the study of the approximate point spectrum of a non‐self‐adjoint operator. The spectrum of a large class of such bounded non‐self‐adjoint operators is studied. The...
The perturbation theory of Hille and Phillips for semigroups of bounded linear operators on a Banach space is modified to apply to the semigroups of positive traceclass operators encountered in quantum statistical mechanics.
The combined gravitational‐neutrino field equations are solved, subject only to the restriction that the energy‐flow vector of the neutrino field be timelike or null. The principal null congruence (pnc) of the neutrino field is necessarily geodesic and shear‐free, and coincides with a...
It is shown that not only some second‐order differential equations, but also some second‐order difference equations (three‐term recurrence relations) possess solutions of WKBJ type. WKBJ‐like solutions are derived and used to study the ``classical'' (large J ) limits of both the 6‐ J...
It is shown that the wavefunctions of the δ‐function l ‐body problem are simple enough to allow an explicit evaluation of the cluster operator U l . Upon integration one can then obtain the general cluster coefficient b l . The l = 2 case is explicitly solved for particles of any statistics.
The structure of local operators linear in the creation and destruction operators of a finite number of particles is investigated. It is shown that these operators determine a set of local and relatively local free fields relative to which the original operators are local. This result is used to...
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