Angular Boson

Consider, furthermore, a (2i- - 1)-dimensional subspace of the Hilbert space with fixed 5. Then, according to Schwinger s theory of angular momentum [98], this discrete spin DoF can be represented by two bosonic oscillators described by creation and annihilation operators with commutation relations... 

The angular momentum (spin) of a particle-like state becomes h/2n for a boson and h/4n for a fermion. 

The result (173) applies to a photon model with the angular momentum h/2n of a boson, whereas the photon radius r would become half as large for the angular momentum h/4 of a fermion. Moreover, the present analysis on superposition of EMS normal modes is applicable not only to narrow linewidth wavepackets but also to a structure of short pulses and soliton-like waves. In these latter cases the radius in Eq. (173) is expected to be replaced by an average value resulting from a spectrum of broader linewidth. 

Last but not least, it must be further investigated whether light manifests itself differently under different conditions. One of these manifestations is represented by an axisymmetric solution of the present theory, which has the nonzero angular momentum of a boson particle. Another is represented by a plane-polarized wave having zero angular momentum. 

The product of angular and spin function must be even under exchange for bosons, and odd for fermions. Moreover, for like pairs the matrix elements that couple the rotovibrational states may be written as... 

In the interacting boson model-2, low lying collective states of nuclei are described in terms of 12 dynamical bosons [ARI77,0TS78], six proton and six neutron bosons. The six proton and neutron bosons have angular momentum J=0 (s-boson) and J=2 (d-boson). It is convenient to introduce creation (d, s ) (u = 2, 1, 0) and annihilation (du,s) operators. When proton ( tt ) and neutron (v) degrees of freedom are added, the creation and annihilation operators assume an extra label ( tt, v), d s, ... 

There is a second, alternative approach. One could assume that the unpaired neutron and the unpaired proton form a quasibound state. The total number of components of the angular momenta of this quasi-bound state is given by n n v. Then we introduce a pair of new bosonic creation and annihilation operators associated with each level of this subsystem, cj, Cj, I,J =... 

The boson creation operators are Ypi where p = iv,v indicates proton or neutron and i = L,M the angular momentum of the basis bosons. We consider even L, even parity for the bosons, which are supposed to represent pairs of like particles (or holes). The numbers Np = Ejnpi are assumed to equal 1/2 the number of proton or neutron particles or holes from the nearest closed shell, and are thus well defined functions of N and Z, to the... 

BEB, 2-BEB etc. We find that such states have much improved angular momentum properties and are not much more difficult to calculate in the HB approximation. In the region above the backbend, where AI for l 0> is increasing rapidly, AI for the state with an excited boson decreases to a minimum. At a still higher spin, the 2-BEB state has the lowest AI value, as seen in Figure 1. 

As described in Ref. [25], the Hartree approach has been applied to get energies and density probability distributions of Br2(X) 4He clusters. The lowest energies were obtained for the value A = 0 of the projection of the orbital angular momentum onto the molecular axis, and the symmetric /V-boson wavefunction, i.e. the Eg state in which all the He atoms occupy the same orbital (in contrast to the case of fermions). It stressed that both energetics and helium distributions on small clusters (N < 18) showed very good agreement with those obtained in exact DMC computations [24],... 

In the case of the q-deformed angular momentum algebra suq( 2) the generators can be mapped onto q-deformed bosons in the following way [23] ... 

It has been shown [31] that the angular momentum operators defined by Eqs (36), expressed in terms of the modified boson operators given by Eq. (45), take the simple form ... 

Here N = N+ + N0 + N- is the total number operator for the -deformed bosons, and the second-order Casimir operator is equal, by definition, to the square of the g-deformed angular momentum operator. These states have the following form... 

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