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A number of sum rules for the optical constants, in particular, the refractive index of a nonconducting medium, are obtained. Some of the sum rule constraints are highly damped for large frequencies, exponentially in one particular case. Formal integral relationships for the index of refraction...
Explicit nonspreading (i.e., characteristically propagating) solutions to a certain class of two‐dimensional, hyperbolic, differential equations are found. This class of equations is a generalization of equations that arose in a study of radiation in cosmological backgrounds.
A systematic study of the symmetry porperties of the Schrödinger equation u x x + i u t = F ( x , t , u , u ∗) is performed. The free particle equation (for F =0) is known to be invariant under the six‐dimensional Schrödinger group S 1 . In this paper we find all continuous subgroups of S 1...
Eigenvalues of the Casimir operators of the orthogonal and the symplectic groups are obtained in closed and simple form by diagonalizing directly the matrices introduced by Perelomov and Popov. This method unifies the treatment of the problem for the semisimple Lie groups.
Sufficient conditions for stability, global asymptotic stability, and explosive instability are established for a class of nonlinear evolutional equations defined in Hilbert spaces by using certain relations between an abstract function and its Gateaux differential. These results are applied to...
Branching rules for the second lowest dimensional representation of the exceptional simple Lie algebra of type E 8 are given with repsect to all its 14 maximal semisimple subalgebras. This representation of E 8 is of dimension 3875, the maximal subalgebras are of types A 8 , D 8 , A 1 ‐ A 7 , A...
The introduction of the group theory in the treatment of the Boltzmann equation shows the reducibility of the collision integral operator on the invariant subspaces of Klein V or SO 2 group. Especially we prove the equality of matrices representing the collision integral operator between...
We use the Weyl quantization W in a general context valid for any finite‐dimensional Lie algebra G , to derive an explicit formula for ( P 1 , P 2 ) ≡ W −1 ( W ( P 1 ), W ( P 2 )), P 1 , P 2 polynomials. In the particular case of the Heisenberg Lie algebra, this formula reduces to the...
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of...
The purpose of this investigation is to find the conditions for characteristic propagation of multipole radiation in Friedmann backgrounds. The radiation fields studied are Klein–Gordon scalar fields, conformally invariant scalar fields, electromagnetic fields, and gravitational fields. The...
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