Kind Of Degeneracy Research Articles

Synthesis of resistive networks from third-order paramount matrices

A new resistive 3-port network configuration capable of realizing any given third-order real symmetric paramount matrix is given. All the edge conductances are explicitly expressed in terms of the entries of the given matrix obviating matrix inversion at any stage of the calculation of the edge conductance values. Also all kinds of degeneracies are taken care of by the explicit formulas given for the edge conductances.

Continuum eigenmodes of an inhomogeneous plasma

The van Kampen-Case treatment of the linearized Vlasov equation is generalized to cases of non-uniform plasmas in non-uniform equilibrium fields. This is done by transforming the Vlasov operator into the representation of the eigenfunctions of the streaming operator. The Vlasov operator is thus reduced to the form of a multiplication operator perturbed by an integral operator so that the continuum eigenfunctions may be constructed by adapting a method originally devised in neutron transport theory. The calculation leads to solving a non-singular Fredholm-type integral equation. Various kinds of degeneracy of the continuous spectrum are discussed and an example is given.

A generalization of field quantization and statistics

Abstract An attempt is made at generalizing commutation relations of creation and annihilation operators in field theory. The algebra for these operators is determined in such a way that they form a basis of representations of either an infinite-dimensional rotation group (R-type) or an infinite-dimensional symplectic group (S-type). The former case leads to a generalized Fermi-Dirac statistics in the sense that at most nmax particles can occupy one and the same state, where nmax is any positive integer. The latter corresponds to a generalization of the Bose-Einstein statistics. Some general properties of many-particles state vectors are investigated. One of the characteristic features in such a theory is that many-particle states show a new kind of degeneracy and form the basis of representations of symmetric group which correspond to the Young diagrams with many rows and columns. It is also shown that in the relativistic field theory the former method (R-type) can be applied only to fields with half-integer spin, whereas the latter method (S-type) can be applied only to fields with integer spin.