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It is shown that a field is a free field as soon as the states generated by the Heisenberg field and the incoming field operators operating on the vacuum coincide statement (i). Several conclusions are drawn from statement (i) concerning the strong convergence of the field for t tending to...
The lattice is a special rooted Cayley tree, generated by N successive m ‐fold branchings. With each point of the tree are associated a mass M and a position coordinate x i . All end points are held fixed at x i =0. The potential energy is V =☒ Σ i,j K ij (x i −x j ) 2 , where K ij =K if i...
The most general dynamical law for a quantum mechanical system is studied with particular reference to the necessary and sufficient conditions for such a law to represent Hamiltonian dynamics. The main results are stated in the form of three theorems.
This is a continuation of Part I with special emphasis on wave equations in an inhomogeneous medium.
Some formal techniques for the study of nonlinear oscillations are illustrated through a development of a general perturbational solution of the harmonically forced van der Pol equation. These techniques provide for the study of perturbations of nearly linear oscillations in almost complete...
The general constitutive equations for galvanomagnetic effects in isotropic materials are applied to the study of electrical conduction in rods. It is shown that, in general, rectilinear current flow is not possible, unless the rod has a circular cross section or is an infinite parallel‐sided...
In this note the Lie algebra generated by the coefficient matrix of a system of ordinary, linear, first‐order differential equations is considered. A systematic discussion, based on some well‐known results in the theory of Lie albegras, is given for the reduction of the problem of integration...
The A‐B‐L theorem states that for almost all density functions the time‐averaged probability of a system being in a region R of an energy shell in phase space is m R /m, where m is the volume of the energy shell and m R is the volume of R. In the present note a stronger form of the...
The notion of generalized free field is introduced, as an obvious extension of a discrete superposition of independent free fields with different masses. The following assumptions are also made: there is an underlying Hilbert space H H (positive‐definite metric), the theory is Lorentz...
A method for calculation of ``principal modes'' of linear or nonlinear systems is discussed. The physical definition of ``principal modes'' is formulated mathematically in two ways. The trial solution of the differential equation of the motion of the system is taken in an appropriate structure....
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