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The n th order index of an irreducible representation of a semisimple compact Lie group, n a nonnegative even integer, is defined as the sum of n th powers of the magnitudes of the weights of the representation. It is shown, in many situations, to have additivity properties similar to those of...
We consider the BBGKY equation for the single particle probability density in a hard sphere system. We investigate whether there is bifurcation from the fluid phase to functions which have crystalline symmetry. We find that as the density of the fluid increases from zero, there is bifurcation in...
We show that an exact dispersion relation can be obtained for a cubic lattice made of spherically‐symmetric attractive potentials. This result is obtained in a limit case where the potentials have zero range and infinite intensity.
In this paper we give a more compact representation of the intelligent spin states defined by Aragone, Guerri, Salamó, and Tani. Using this new representation, we discuss the differences between minimum uncertainty states, coherent Bloch spin states and intelligent states. The evolution of these...
In a space of four dimensions I determine all possible second‐order vector–tensor field equations which are derivable from a variational principle, compatible with the notion of charge conservation and in agreement with Maxwell’s equations in a flat space. The general solution to this...
A recent paper of Kasperkovitz and Dirl J. Math. Phys. 15, 1203 (1974) concerning the tensor representation for compact groups is examined critically. The flaw which is found in the main theorem fortunately does not affect the deductions which are made from that theorem.
The isotropic multigroup transport equation is solved in L p , p ≳1, for both half range and full range problems, using resolvent integration techniques. The connection between these techniques and a spectral decomposition of the transport operator is indicated.
By constructing the one‐parameter group of automorphisms generated by a typical derivation and generalizing certain special cases arising, we find all the automorphisms of the Lie algebra of polynomials under Poisson bracket. We introduce the notion of quasi‐Hamiltonian equations, and...
All the Clebsch–Gordan coefficients for SU(4) that would be required for particle physics, including those decomposed with respect to SU(3), are obtained by using the general formalism of Baird and Biedenharn.
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