Combinations Of Bosons Research Articles

Extended General Relativity: (3+1)-anyons in a preinflationary cosmological model

We propose an extended General Relativistic formalism with boundary terms included, that describes the dynamics of quantum spinor fields, which can take intermediate values, named (3+1)-anyons. In the approach here worked, we use an extended manifold in which the left( 3+1right) -anyon fields can be expressed as a linear combination of bosons and fermions. We calculate the flow of these fields with self-interactions included in a preinflationary model that describes the birth of the universe from a null Hubble parameter, and we obtain the value of the cosmological parameter at this moment due to the flux of (3+1)-anyons through the 3d-closed hypersurface. The spectral indices at the end of preinflation are in very good agreement with observations. In particular the tensor to scalar ratio obtained at the end of preinflation is very small: r(phi _*) = 0.00336.

3D reduction of the N-body Bethe–Salpeter equation

We perform a 3D reduction of the two-fermion homogeneous Bethe–Salpeter equation, by series expansion around a positive-energy instantaneous approximation of the Bethe–Salpeter kernel, followed by another series expansion at the 3D level in order to get a manifestly hermitian 3D potential. It turns out that this potential does not depend on the choice of the starting approximation of the kernel anymore, and can be written in a very compact form. This result can also be obtained directly by starting with an approximation of the free propagator, based on integrals in the relative energies instead of the more usual δ-constraint. Furthermore, the method can be generalized to a system of N particles, consisting in any combination of bosons and fermions. As an example, we write the 3D equation for systems of two or three fermions exchanging photons, in Feynman or Coulomb's gauge.

A representation of a higher spin N=2 conformal algebra

Abstract The free field representations of the nonlinear N=2 W∞ algebra is shown to exist. It is found that the bosonic sector possesses W 1+∞ ⊕ W ∞ structure. But in terms of the free fields, both types of the bosonic generators are required to be represented as suitable combinations of bosons and fermions, unlike the linear representation of the N=2 W∞ algebra. In the fermionic sector, both the fermions possess exponential type representations in the free fields, in general.

Parafermion statistics and quasihole excitations for the generalizations of the paired quantum Hall states

We continue the program started in cond-mat/9809384 and explain the statistics of the excitations for the generalizations of the paired states in the quantum Hall effect in terms of the parafermion statistics. We show that these excitations behave as combinations of bosons and parafermions. That generalizes the prior treatment of the paired (Pfaffian) state where the excitations behave as combinations of bosons and fermions. We explain what it means, from a quantum mechanical point of view, for a particle to be a `parafermion' rather than a boson or a fermion and work through several explicit examples. The resulting multiplets coincide exactly with the angular momentum multiplets found numerically for the $k+1$ particle interaction Hamiltonian on a sphere. We also present a proof that the wave functions found in cond-mat/9809384 are indeed the correlation functions of the parafermion conformal field theory.