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New aspects of the Z Z-graded 1D superspace: induced strings and 2D relativistic models
A novel feature of the -graded
supersymmetry which finds no counterpart in ordinary supersymmetry is the
presence of -graded exotic bosons (implied by the existence of two classes
of parafermions). Their interpretation, both physical and mathematical,
presents a challenge. The role of the "exotic bosonic coordinate" was not
considered by previous works on the one-dimensional -graded superspace (which was restricted to produce
point-particle models). By treating this coordinate at par with the other
graded superspace coordinates new consequences are obtained. The graded
superspace calculus of the -graded worldline
super-Poincar\'e algebra induces two-dimensional -graded relativistic models; they are invariant under a new -graded super-Poincar\'e algebra which differs
from the previous two -graded versions
of super-Poincar\'e introduced in the literature. In this new superalgebra the
second translation generator and the Lorentz boost are -graded.
Furthermore, if the exotic coordinate is compactified on a circle ,
a -graded closed string with periodic
boundary conditions is derived. The analysis of the irreducibility conditions
of the supermultiplet implies that a larger -deformed, where
is a real parameter) class of point-particle models than the ones
discussed so far in the literature (recovered at ) is obtained. While
the spectrum of the point-particle models is degenerate (due to its
relation with an supersymmetry), this is no longer the case for
the models.Comment: 28 page
On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
We investigate supergroups with Grassmann parameters replaced by odd Clifford
parameters. The connection with non-anticommutative supersymmetry is discussed.
A Berezin-like calculus for odd Clifford variables is introduced. Fermionic
covariant derivatives for supergroups with odd Clifford variables are derived.
Applications to supersymmetric quantum mechanics are made. Deformations of the
original supersymmetric theories are encountered when the fermionic covariant
derivatives do not obey the graded Leibniz property. The simplest non-trivial
example is given by the N=2 SQM with a real multiplet and a cubic
potential. The action is real. Depending on the overall sign ("Euclidean" or
"Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian
hamiltonian is encountered when solving the equation of motion of the auxiliary
field. A possible connection of our framework with the Drinfeld twist
deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page
Compliance of modern trends in juvenile justice with the provisions of the Convention on the Rights of the Child
В статье рассматривается соответствие основных положений ювенальной юстиции положениям Конвенции о правах ребенка, выявлены достоинства и противоречия данного направления юстиции.The article discusses the compliance of juvenile justice with the Convention on the Rights of the Child, identifies the advantages and disadvantages of this area of justice
Changing parameters immune system in children with different forms of early congenital syphilis
The results of immunological monitoring of 40 children with early congenital syphilis in the acute period and after specific therapy. Revealed that the severity of changes in the immune system depend on the clinical form of the disease and the most significant group of children with polisimptomnym over syphilitic infection. The majority of the investigated immunological parameters after specific therapy in patients of this group are not restored to control values, which can be regarded as serious, not smooth during desease. Babies with early monosemeiotic form of congenital syphilis immunological indicators partially recovered, indicating a possible protracted course of the process. At the same time, patients with latent form of the disease immunological parameters restored to control values, which suggesta favorable prognosis
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