292 research outputs found
A Lesson Plan with an Arc Midpoint
The article introduces an explicit way of locating the arc midpoint in the Cartesian plane, which is consistent for both x- and y-coordinates and is technically accessible for students starting as young as fifteen. The authors give the proof of the statement using two trigonometry identities, and discuss some materials for innovative lessons on the arc midpoint computation that could enrich and enhance curriculum
Nilpotent Marsh and SUSY QM
We consider the nilpotent additions to classical trajectories in
supersymmetric and nonsupersymmetric theories. The condition of anilpotence of
action on some generalized solutions leads to the Witten supersymmetric
Lagrangian. The condition of anilpotence of topological charge is the same as
one of superpotential with spontaneous broken supersymmetry. We should vanish
half of Grassmann constants of integration, because in this case only we obtain
the same number of normalized bosonic and fermionic zero modes.Comment: 8 pages, Latex 2.09. Talk given at the conference in memory of V.I.
Ogievetski, Dubna, July, 1997. To be published in the Proceeding
D=10 super-D9-brane
Superfield equations of motion for D=10 type IIB Dirichlet super-9-brane are
obtained from the generalized action principle. The geometric equations
containing fermionic superembedding equations and constraints on the
generalized field strength of Abelian gauge field are separated from the proper
dynamical equations and are found to contain these dynamical equations among
their consequences. The set of superfield equations thus obtained involves a
Spin(1,9) group valued superfield h_\a^{~\b} whose leading component appears
in the recently obtained simplified expression for the kappa-symmetry projector
of the D9-brane. The Cayley image of this superfield coincides (on the mass
shell) with the field strength tensor of the world volume gauge field
characteristic for the Dirichlet brane. The superfield description of the
super-9-brane obtained in this manner is known to be, on the one hand, the
nonlinear (Born-Infeld) generalization of supersymmetric Yang-Mills theory and,
on the other hand, the theory of partial spontaneous breaking of D=10, N=IIB
supersymmetry down to D=10, N=1.Comment: 34 pages, LATEX. Minor corrections. References adde
New records of Dacrymyces ovisporus and Tremella diaporthicola from the Ukraine
The present paper deals with new records of the heterobasidioid fungi Dacrymyces ovisporus Bref. and Tremella diaporthicola Ginns et M.N.L. Lefebvre in Europe. The taxonomical status of these species is considered and detailed descriptions and illustrations of specimens are given
Potentials in N=4 superconformal mechanics
Proceeding from nonlinear realizations of (super)conformal symmetries, we
explicitly demonstrate that adding the harmonic oscillator potential to the
action of conformal mechanics does not break these symmetries but modifies the
transformation properties of the (super)fields. We also analyze the possibility
to introduce potentials in N=4 supersymmetric mechanics by coupling it with
auxiliary fermionic superfields. The new coupling we considered does not
introduce new fermionic degrees of freedom - all our additional fermions are
purely auxiliary ones. The new bosonic components have a first order kinetic
term and therefore they serve as spin degrees of freedom. The resulting system
contains, besides the potential term in the bosonic sector, a non-trivial
spin-like interaction in the fermionic sector. The superconformal mechanics we
constructed in this paper is invariant under the full
superconformal group. This invariance is not evident and is achieved within
modified (super)conformal transformations of the superfields.Comment: 12 pages, PACS number: 12.60.J
Diffeomorphism, kappa transformations and the theory of non-linear realisations
We will show how the theory of non-linear realisations can be used to
naturally incorporate world line diffeomorphisms and kappa transformations for
the point particle and superpoint particle respectively. Similar results also
hold for a general p-brane and super p-brane, however, we must in these cases
include an additional Lorentz transformation.Comment: 19pages, no figure. References are added and typos are correcte
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