Projective Hilbert space structures at exceptional points

Projective Hilbert space structures

A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseuxexpanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular b...

Hilbert Schemes of Points in Projective Spaces

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...

Projective Group Representations in Quaternionic Hilbert Space

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...

Exceptional Points of an Endomorphism of the Projective Plane