2,492 research outputs found
Classification of the GL(3) Quantum Matrix Groups
We define quantum matrix groups GL(3) by their coaction on appropriate
quantum planes and the requirement that the Poincare series coincides with the
classical one. It is shown that this implies the existence of a Yang-Baxter
operator. Exploiting stronger equations arising at degree four of the algebra,
we classify all quantum matrix groups GL(3). We find 26 classes of solutions,
two of which do not admit a normal ordering. The corresponding R-matrices are
given.Comment: 28 pages, Late
Tachyon condensation in cubic superstring field theory
It has been conjectured that at the stationary point of the tachyon potential
for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density
cancels the brane tension. We study this conjecture using a cubic superstring
field theory with insertion of a double-step inverse picture changing operator.
We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case
we obtain that the value of the potential at the minimum is 97.5% of the non
BPS D-brane tension. Using a special gauge in the second case we get 105.8% of
the tension.Comment: 19 pages, LaTeX, 3 figures. Eqs. (3.2), (3.3) and (4.6) are
corrected, and new gauge fixing condition is use
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
In this work we study the centers of planar analytic vector fields which are
limit of linear type centers. It is proved that all the nilpotent centers are
limit of linear type centers and consequently the Poincar\'e--Liapunov method
to find linear type centers can be also used to find the nilpotent centers.
Moreover, we show that the degenerate centers which are limit of linear type
centers are also detectable with the Poincar\'e--Liapunov method.Comment: 24 pages, no figure
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