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A SU(2) recipe for mutually unbiased bases
A simple recipe for generating a complete set of mutually unbiased bases in
dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed
from a single matrix acting on a space of constant angular momentum j and
defined in terms of the irreducible characters of the cyclic group C(2j+1). As
two pending results, this matrix is used in the derivation of a polar
decomposition of SU(2) and of a FFZ algebra.Comment: v2: abstract enlarged, a corollary added, acknowledgments added, one
reference added, presentation improved; v3: two misprints correcte
A [SU(6)] FLAVOR MODEL WITHOUT MIRROR FERMIONS
We introduce a three family extension of the Pati-Salam model which is
anomaly-free and contains in a single irreducible representation the known
quarks and leptons without mirror fermions. Assuming that the breaking of the
symmetry admits the implementation of the survival hypothesis, we calculate the
mass scales using the renormalization group equation. Finally we show that the
proton remains perturbatively stable.Comment: Z PHYS. C63, 339 (1994
Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach
We study the quantum Hall effect in graphene at filling factors \nu = 0 and
\nu = \pm, concentrating on the quantum Hall ferromagnetic regime, within a
non-perturbative bosonization formalism. We start by developing a bosonization
scheme for electrons with two discrete degrees of freedom (spin-1/2 and
pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases
are considered, namely the so-called spin-pseudospin, spin, and pseudospin
phases. The first corresponds to a quarter-filled (\nu =-1) while the others to
a half-filled (\nu = 0) lowest Landau level. In each case, we show that the
elementary neutral excitations can be treated approximately as a set of
n-independent kinds of boson excitations. The boson representation of the
projected electron density, the spin, pseudospin, and mixed spin-pseudospin
density operators are derived. We then apply the developed formalism to the
effective continuous model, which includes SU(4) symmetry breaking terms,
recently proposed by Alicea and Fisher. For each quantum Hall state, an
effective interacting boson model is derived and the dispersion relations of
the elementary excitations are analytically calculated. We propose that the
charged excitations (quantum Hall skyrmions) can be described as a coherent
state of bosons. We calculate the semiclassical limit of the boson model
derived from the SU(4) invariant part of the original fermionic Hamiltonian and
show that it agrees with the results of Arovas and co-workers for SU(N) quantum
Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking
terms in the skyrmion energy.Comment: 16 pages, 4 figures, final version, extended discussion about the
boson-boson interaction and its relation with quantum Hall skyrmion
Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
Inspired by the four-fold spin-valley symmetry of relativistic electrons in
graphene, we investigate a possible SU(4) fractional quantum Hall effect, which
may also arise in bilayer semiconductor quantum Hall systems with small Zeeman
gap. SU(4) generalizations of Halperin's wave functions [Helv. Phys. Acta 56,
75 (1983)], which may break differently the original SU(4) symmetry, are
studied analytically and compared, at nu=2/3, to exact-diagonalization studies.Comment: 4+epsilon pages, 4 figures; published version with minor correction
Models of Dynamical Supersymmetry Breaking from a SU(2k+3) Model
We investigate three classes of supersymmetric models which can be obtained
by breaking the chiral SU(2k+3) gauge theories with one antisymmetric tensor
and 2k-1 antifundamentals. For N=3, the chiral SU(2k)SU(3)U(1)
theories break supersym metry by the quantum deformations of the moduli spaces
in the strong SU(2k) gauge coupling limit. For N=2, it is the generalization of
the SU(5)U(2)U(1) model mentioned in the literature.
Supersymmetry is broken by carefully choosing the q uark-antiquark-doublet
Yukawa couplings in this model. For N=1, this becomes the well-known model
discussed in the literature.Comment: 13 pages, modifications to the sections two and thre
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