4 research outputs found
Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge
The present work proposes a discussion on the self-energy of charged
particles in the framework of nonlinear electrodynamics. We seek magnet- ically
stable solutions generated by purely electric charges whose electric and
magnetic fields are computed as solutions to the Born-Infeld equa- tions. The
approach yields rich internal structures that can be described in terms of the
physical fields with explicit analytic solutions. This suggests that the
anomalous field probably originates from a magnetic excitation in the vacuum
due to the presence of the very intense electric field. In addition, the
magnetic contribution has been found to exert a negative pressure on the
charge. This, in turn, balances the electric repulsion, in such a way that the
self-interaction of the field appears as a simple and natural classical
mechanism that is able to account for the stability of the electron charge.Comment: 8 pages, 1 figur
Combinatorial realizations of crystals via torus actions on quiver varieties
Consider Kashiwara's crystal associated to a highest weight representation of
a symmetric Kac-Moody algebra. There is a geometric realization of this object
using Nakajima's quiver varieties, but in many particular cases it can also be
realized by elementary combinatorial methods. Here we propose a framework for
extracting combinatorial realizations from the geometric picture: We construct
certain torus actions on the quiver varieties and use Morse theory to index the
irreducible components by connected components of the subvariety of torus fixed
points. We then discuss the case of affine sl(n). There the fixed point
components are just points, and are naturally indexed by multi-partitions.
There is some choice in our construction, leading to a family of combinatorial
models for each highest weight crystal. Applying this construction to the
crystal of the fundamental representation recovers a family of combinatorial
realizations recently constructed by Fayers. This gives a more conceptual proof
of Fayers' result as well as a generalization to higher level. We also discuss
a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some
references; v3: many small correction