Gotowa bibliografia na temat „Interacting Bosons (two Spin State)”

The simplest of the two-body random matrix ensembles (TBRE) is the embedded Gaussian orthogonal ensemble of two-body interactions [EGOE(2)] for spinless fermion systems. With m fermions in N single particle states, EGOE(2) and similarly EGUE(2) [the embedded Gaussian unitary ensemble] are generated by the SU(N) algebra. For these ensembles results, obtained using SU(N) Wigner-Racah algebra, for lower order cross correlations between spectra with different particle numbers are given. For fermions with spin degree of freedom one has EGOE(2)-s and similarly EGUE(2)-s, both generated by U(2Ω) ⊃ U(Ω) ⊗ SU(2) algebra with SU(2) generating m particle spins S and 2Ω = N. For these ensembles numerical and first analytical results for cross correlations between spectra with different particle numbers and spins are given. As further extensions, it is possible to construct EGOE(2)-(s,p) generated by U(2Ω) ⊃ [U(Ω) ⊃ SO(Ω)] ⊗ SU(2) where SO(Ω) corresponds to pairing, for nuclear shell model the EGOE(2)-JT generated by U(N) ⊃ SOJ(3) ⊗ SUT(2) algebra etc. On the other hand EGOE's with extended group symmetries of the shell model and the interacting boson models of nuclei, in particular via trace propagation for energy centroids give new insights into regular structures seen in the ground state region of nuclei. Several new examples for energy centroids generated by random 2 and 3-body interactions are given.

The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.

We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an N=6 supergravity multiplet, with the preons and antipreons both in the 20 of SU(6). Hypercolor singlets are forbidden in the fermionic sector of this theory; we propose that the SU(4) symmetry spontaneously breaks to SU (3)× U (1), with the binding of triality nonzero preons and gluons into composites, and with the formation of a color singlet condensate that breaks the initial Z12 vacuum symmetry to Z6. The spin ½ fermionic composites have the triality structure of a quark–lepton family, and the initial Z12 symmetry implies that there are six massless families, which mix to give three distinct families below the scale of the condensate. The spin 1 triality zero composites of the color triplet SU(4) gluons, when coupled to the condensate and with the color singlet representation of the 10 acting as a doorway state, lead to weak interactions of the fermionic composites through an SU(2) gauge algebra. The initial Z12 symmetry implies that this SU(2) gauge algebra structure is doubled, which in turn permits the corresponding independent gauge bosons to couple to chiral components of the composite fermions. Since the U(1) couples to the 10 representation as B-L, an effective SU (2)L× SU (2)R × U (1)B-L electroweak theory arises at the condensate scale, with all composites having the correct electric charge structure. Assuming a mechanism for forming composite Higgs bosons, the Z12→ Z6 symmetry breaking chain implies that below the condensate scale there can be two sets of discrete chiral Z6 triplets of Higgs doublets, as required by a phenomenological model for the CKM matrix that we have analyzed in detail elsewhere. A renormalization group analysis of the SU(4) model shows that the conversion by binding of one 10 of SU(4) to 12 triplets of SU(3) can give a very large, calculable hierarchy ratio between the SU(4) and the hadronic mass scales.

If special relativity is a dynamic symmetry caused by true physical deformations of bodies in absolute motion through a substratum or ether, the question if all interactions and elementary particles arc excitations of this ether must be raised. The ether being the cause of all the observed relativistic effects should then obey an exactly nonrelativistic law of motion, and which permits it to consist of positive and negative masses. The fundamental constants of nature, which according to Planck are 1) Newton's constant (G), 2) the velocity of light (c) and 3) Planck’s constant (ћ), suggest that the ether is made up of densely packed positive and negative Planck masses (Planckions), each with a diameter equaling the Planck length. Symmetry demands that the number of positive and negative Planck masses should be equal, making the cosmological constant equal to zero. Because the Planckions are nonrelativistic spin-zero bosons, the ether would therefore consist of two super­fluids, one for the positive mass Planckions, and the other one for the negative mass Planckions. By spontaneous symmetry breaking this superfluid ether can in its ground state form a lattice of small vortex rings, with the vortex core radius equaling the Planck length. Force fields of massless vector gauge bosons can be interpreted as quantized transverse vortex waves propagating through this lattice. Because the smallest wave length would be about equal the ring radius of the circular vortices, the ring radius would assume the role of a unification scale. The ring radius is estimated to be about 103 times the Planck length, in fairly good agreement with the empirical evidence for the value of the grand unification scale of the standard model.Charge is explained by the zero point fluctuations of the Planckions attached to the vortex rings, wrhich thereby become the source of virtual phonons. Charge quantization is explained as the result of circulation quantization. Spinors result from bound states of the positive and negative masses of the substratum, and special relativity as a dynamic symmetry would be valid for all those objects. Quantum electrodynamics is derived as a low energy approximationIf spinors are made up from the positive and negative masses of the vortex ring resonance energy, whereby the spinors would assume the character of excitons, the spinor mass can be computed in terms of the Planck mass. Vice versa, with the lowest quark mass m given, a value for the gravitation­al constant in terms of m, ћ, and c can be obtained. The existence of different particle families can be understood by internal excitations of the spinors, and parity violation may find its explanation in a small nonzero vorticity of the ether. Bacause of its simple fundamental symmetry the theory is unique, it is always finite and has no anomalies.In the proposed theory all fields and interactions are explained in a completely mechanistic way by the Planck masses and their contact interactions. With special relativity as a derived dynamic symmetry and space remaining euclidean, the proposed approach can be seen as an alternative to Einstein’s program to explain all fields and their interactions by symmetries and singularities of a noneuclidean spacetime manifold.In Part I, the fundamental equation for the substratum, which has the form of a nonrelativistic nonlinear Heisenberg equation, is formulated. It is shown how it leads to a Maxwell-type set of equations for the gauge bosons. In Part II, Dirac-type spinors and quantum electrodynamics are derived. These results are then applied to obtain the lowest quark mass in terms of the Planck mass.