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The level density of a degenerate Fermi system is modified by the perturbation in the position of a single‐particle level. To study this effect, miscellaneous exact relations between the level densities of the perturbed and unperturbed system are derived. For the special case of the perturbed...
An algebraic classification of four‐dimensional Riemann spaces with signature ‐2 is given. The possible Riemann and Ricci tensors are listed and inversion formulas from one to the other are obtained. Classifications are given for the two special spaces R ij = 0 and R k l R m k = 0 R k l R m k...
The Newman‐Penrose formalism for obtaining the recent conserved quantities in general relativity is discussed and a group‐theoretic interpretation is given to it. This is done by relating each triad of the orthonormal vectors on the sphere to an orthogonal matrix g . As a result, the...
A Riemannian space V n is said to admit a particular symmetry which we call a ``curvature collineation'' (CC) if there exists a vector ξ i for which ξ R j k m i = 0 ξ R j k m i = 0 , where R j k m i R j k m i is the Riemann curvature tensor and £ ξ denotes the Lie derivative. The...
Drawing on the understanding of unitarity integrals acquired in previous papers J. Math. Phys. 10, 494, 545 (1969), we show that unitarity demands that connected amplitudes be singular on the positive‐α arcs of all ``simple'' Landau curves in their physical regions. Further, we show that the...
A new approach to the solution of transport problems, based on the ideas introduced into transport theory by Ambarzumian, Chandrasekhar, and Case, is discussed. To simplify the discussion, the restriction to plane geometry and one‐speed isotropic scattering is made. However, the method can be...
An effective Hamiltonian is derived which describes the relative motion of two oppositely charged particles in a homogeneous magnetostatic field.
This paper considers the determination of N ‐representability (for diagonal elements) of p ‐density matrices restricted to certain finite‐dimensional subspaces of l 2 of the configuration space of N identical antisymmetric particles. In particular, an arbitrary set of N + p spin orbitals is...
A set of linear inequalities for the reduced two‐body density matrix is presented. The general problem of finding all such inequalities is discussed. It is shown that all of the linear inequalities found so far for ensemble representability may be written as a single family of inequalities.
The theory of a quantized Dirac field interacting with a classical electromagnetic field is considered. The resulting q ‐number problem is reduced to a closely related c ‐number problem. The theory is then shown to be without divergences. The interpolating field is shown to exist and is...
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