Spinors and space-time

SPINORS and SPACE – TIME ANISOTROPY

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...

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...

A Note on Dirac Spinors in a Non-flat Space-time of General Relativity

Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field. 1. Algebra and geometry of two-component spinors. From a mathematical point of view two-component spinors naturally arise when one tries to understand geometrically the well-known group homomorphism φ : SL(2,C) → SO(1, 3,R) (1.1) given by the following expl...

SPINORS and