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It is shwn that the energy spectrum of the Bloch electron in an external field is continuous. Furthermore, it is shown that all approximations which take into account interband coupling whithin groups of finite number of bands (the N ‐band approximation) lead to a pure‐point spectrum of...
A unique two‐component spinor connection, which we call the standard connection, is determined by the requirement that it be compatible with the spinor inner product and that it give rise to the standard 4‐vector connection. Here we take the most general spinor connection, presuming that the...
A rank‐two tensor is built out of the 4‐velocities of two inertial observers, which corresponds precisely to the most general Lorentz matrix connecting the two Cartesian frames of the observers. The Lorentz tensor is then factorized as the product of two ’’complementary’’ space‐time...
The complex‐energy distorted plane waves for scattering via a general class of two‐body Coulomb‐like potentials are shwn to satisfy off‐energy‐shell Lippmann‐Schwinger equaions in the case of two particle scattering and appropriately iterated Weinberg‐Van Winter and Faddeev...
We consider the Yukawa 2 model with (relativistic) interaction density λψΓψϕ+μϕ, where Γ=1 or γ 5 . For sufficiently large μ, we apply the Glimm–Jaffe–Spencer cluster expansion to construct the infinite volume theory satisfying the Wightman and Osterwalder–Schrader axioms...
In general when one writes a relativistic wave equation of the form (− i Γ⋅∂+ m ) ψ ( x ) =0, that transforms covariantly under some representation Λ→ T (Λ) of SL(2, C ), it is nontrivial to determine whether or not the equation is irreducible or to avoid ending up with a reducible...
With the help of the Phragmén‐Lindelöf theorem, we can rederive the full Jin‐Martin’s results on the total cross section lower bound.
We examine a class of two‐dimensional Lorentz manifolds which are ’’singular’’ in a certain sense. It is shown that, for such a manifold ( M , g ), the bundle boundary is a single point whose only neighborhood is all of M ̄ the bundle completion of M ; see B. G. Schmidt, Gen. Rel....
Simple phase‐integral formulas for the calculation, without the use wavefunctions, of quantal matrix elements of multiplicative and differential operators are given for the case of bound states in a single‐well potential. The matrix elements are obtained to within the accuracy corresponding...
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