15,505 research outputs found

### A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra

In this article we consider linear operators satisfying a generalized
commutation relation of a type of the Heisenberg-Lie algebra. It is proven that
a generalized inequality of the Hardy's uncertainty principle lemma follows.
Its applications to time operators and abstract Dirac operators are also
investigated

### Color Superconductivity in N=2 Supersymmetric Gauge Theories

We study vacuum structure of N=2 supersymmetric (SUSY) QCD, based on the
gauge group SU(2) with N_f=2 flavors of massive hypermultiplet quarks, in the
presence of non-zero baryon chemical potential (\mu). The theory has a
classical vacuum preserving baryon number symmetry, when a mass term, which
breaks N=2 SUSY but preserves N=1 SUSY, for the adjoint gauge chiral multiplet
(m_{ad}) is introduced. By using the exact result of N=2 SUSY QCD, we analyze
low energy effective potential at the leading order of perturbation with
respect to small SUSY breaking parameters, \mu and m_{ad}. We find that the
baryon number is broken as a consequence of the SU(2) strong gauge dynamics, so
that color superconductivity dynamically takes place at the non-SUSY vacuum.Comment: 15 pages, 9 figures, a figure and discussions added in Sec. 4,
version to appear in Phys. Rev.

### Meta-stable Vacuum in Spontaneously Broken N=2 Supersymmetric Gauge Theory

We consider an N=2 supersymmetric SU(2) \times U(1) gauge theory with N_f=2
massless flavors and a Fayet-Iliopoulos (FI) term. In the presence of the FI
term, supersymmetry is spontaneously broken at tree level (on the Coulomb
branch), leaving a pseudo-flat direction in the classical potential. This
vacuum degeneracy is removed once quantum corrections are taken into account.
Due to the SU(2) gauge dynamics, the effective potential exhibits a local
minimum at the dyon point, where not only supersymmetry but also U(1)_R
symmetry is broken, while a supersymmetric vacuum would be realized toward
infinity with the runaway behavior of the potential. This local minimum is
found to be parametrically long-lived. Interestingly, from a phenomenological
point of view, in this meta-stable vacuum the massive hypermultiplets inherent
in the theory play the role of the messenger fields in the gauge mediation
scenario, when the Standard Model gauge group is embedded into their flavor
symmetry.Comment: 27 pages, 11 figures, journal reference added, minor modifications in
the tex

### Field evolution of the magnetic structures in Er$_2$Ti$_2$O$_7$ through the critical point

We have measured neutron diffraction patterns in a single crystal sample of
the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase
(T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the
[110] direction. We determine all the characteristics of the magnetic structure
throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er
moments align along the field at $H_c$ and their values reach a minimum. Using
a four-sublattice self-consistent calculation, we show that the evolution of
the magnetic structure and the value of the critical field are rather well
reproduced using the same anisotropic exchange tensor as that accounting for
the local paramagnetic susceptibility. In contrast, an isotropic exchange
tensor does not match the moment variations through the critical point. The
model also accounts semi-quantitatively for other experimental data previously
measured, such as the field dependence of the heat capacity, energy of the
dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

### Massive Hyper-Kahler Sigma Models and BPS Domain Walls

With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we
give the massive Hyper-Kahler sigma models that are not toric in the N=1
superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of
flavors) discrete vacua that may allow various types of domain walls, whereas
the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution
in the case of N=2 and M=1 in the U(M) quotient model.Comment: 16 pages, 1 figure, contribution to the Proceedings of the
International Conference on "Symmetry Methods in Physics (SYM-PHYS10)" held
at Yerevan, Armenia, 13-19 Aug. 200

### Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation
relation $[\Theta,H]=i$, and thus it may be thought of as being canonically
conjugate to the Hamiltonian $H$. The time operator associated with a given
Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+
\Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition
$[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of
$\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the
eigenstate basis. This calculation requires the summation of divergent series,
and the summation is accomplished by using zeta-summation techniques. It is
shown that by including appropriate homogeneous contributions, the matrix
elements of $\Theta$ simplify dramatically. However, it is still not clear
whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

### On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I

In this paper, we consider the spectrum of a model in quantum electrodynamics
with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint;
(2) under the infrared regularity condition, the Hamiltonian has a unique
ground state for sufficiently small values of coupling constants. The spectral
scattering theory is studied as well and it is shown that asymptotic fields
exist and the spectral gap is closed

### Reasons for Home Schooling in Canada

Why do parents in Canada choose to home school their children? This article presents the results of qualitative interviews with 23 home-schooling families in Ontario and British Columbia and compares these results with previous research in other jurisdictions, particularly the United States. The findings suggest that Canadian home-based educators have very different reasons for choosing home schooling than their U.S. counterparts. Possible explanations for these differences are discussed. Dans cet article, lâ€™auteur prÃ©sente les rÃ©sultats dâ€™entrevues qualitatives auprÃ¨s de 23 familles de lâ€™Ontario et de la Colombie-Britannique qui ont optÃ© pour lâ€™ensei- gnement Ã domicile et compare ces rÃ©sultats avec ceux de recherches menÃ©es aux Ã‰tats-Unis. Il semble que les parents canadiens nâ€™aient pas du tout les mÃªmes raisons dâ€™opter pour lâ€™enseignement Ã domicile que les parents amÃ©ricains. Lâ€™auteur propose des explications.

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