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The relationship between the Poincaré and Galilei groups allows us to write the Poincaré wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.
In a previous paper (I) we studied the interrelations between the coefficients of Fokker–Planck equations associated to a restricted class of Langevin equations. We now discuss the general case of an arbitrary state‐dependent diffusion matrix D, which, in particular, may be singular. Moreover...
A density matrix method is used to obtain an exact solution for the reduced density matrix of the field in an arbitrary multimode m ‐photon absorption process. The results of some earlier specialized studies of photon statistics in multiphoton absorption process can be recovered from this...
The Hauser metric is found in the canonical form obtained by Halford for a vacuum metric of Petrov type N admitting a two parameter group of homothetic motions. A result concerning the symmetries of vacuum metrics of Petrov type N possessing twisting geodesic rays is corrected.
Expressions connecting nonscalar R(3) products of operators which shift the eigenvalues of the R(3) Casimir operator L 2 are constructed within the R(2λ+1) groups (λ=2 or 3).
The quasisteady model, derived by the author in an earlier paper, is extended to include lateral boundary conditions. The approach is to first specify a complete time‐dependent problem, including boundary conditions; it is stressed that to each boundary condition there should be associated a...
An explicit solution is presented for a special case of the problem of determining the cross spectral density of a radiation source from its far‐field intensity pattern. The case considered is that of a flat, circular source radiating into a half‐space, where the source coherence properties...
We discuss time evolution operator for N interacting quantum harmonic oscillators and determine certain conditions under which an explicit closed‐form expression can be found for this time‐ordered operator. The special case of N =2 is discussed, as an example.
A theory of n scalar fields is outlined in which the equations of motion are invariant under all nonsingular global transformations of the fields amongst themselves, whether linear or nonlinear.
The formal solutions of certain three‐dimensional inverse scattering problems presented in papers I and II of this series J. Math. Phys. 10, 1819 (1969); 17 1175 (1976) are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When...
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