Spinors of 13-dimensional space

SPINORS and SPACE – TIME ANISOTROPY

Projective Statistics and Spinors in Hilbert Space

In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly projective representation is highly non-trivial, of dimension 2 N−1 2 , and is most easily realized starting with spinor geometry. Quasiparticles in the Pfaffian q...

Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions

We derive a Weierstrass-type formula for conformal Lagrangian immersions in Euclidean 4-space, and show that the data satisfies an equation similar to Dirac equation with complex potential. Alternatively this representation has a simple formulation using quaternions. We apply it to the Hamiltonian stationary case and construct all possible tori, thus obtaining a first approach to a moduli space...

Spinors, Superalgebras and the Signature of Space-time

Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the R-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension D ≤ 11. These theories are re...

BPS Solitons and Killing Spinors in Three Dimensional

In the framework of three dimensional extended supergravity theories, we demonstrate that there exist non-trivial Killing spinors over BPS soliton configurations, even when the space-time is asymptotically conical. We also show that there are no physical fermionic zero modes on these backgrounds. We further generalize these results to the case of semilocal systems. The connection between Bogomo...