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Register a new userAnalyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field
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We study a neutral atom with a non-vanishing electric dipole moment coupled to the quantized electromagnetic field. For a sufficiently small dipole moment and small momentum, the one-particle (self-) energy of an atom is proven to be a real-analytic function of its momentum. The main ingredient of our proof is a suitable form of the Feshbach-Schur spectral renormalization group.
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There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary contribution to the retarded solution for the {em potential} can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation governing the {em field} may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a source whose distribution pattern both rotates and travels faster than light {em in vacuo}, as realized in recent experiments, the boundary term in the retarded solution governing the field is by a factor of the order of $R^{1/2}$ {em larger} than the source term of this solution in the limit that the distance $R$ of the boundary from the source tends to infinity. This result is consistent with the prediction of the retarded potential that part of the radiation field generated by a rotating superluminal source decays as $R^{-1/2}$, instead of $R^{-1}$, a prediction that is confirmed experimentally. More importantly, it pinpoints the reason why an argument based on a solution of the wave equation governing the field in which the boundary term is neglected (such as appears in the published literature) misses the nonspherical decay of the field.
We compute the density of states for the Cauchy distribution for a large class of random operators and show it is analytic in a strip about the real axis.
We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstrom systems which describe large particle ensembles interacting by either electromagnetic fields or a relativistic scalar gravity model. For both systems we derive a radiation formula analogous to the Einstein quadrupole formula in general relativity.
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schrodinger operator with a potential of finite support are derived. This includes a careful analysis of the band edge singularities and allows to prove a Levinson-type theorem. The main algebraic tool are the plane wave transfer matrices.
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