2,320 research outputs found
Localization in Nets of Standard Spaces
Starting from a real standard subspace of a Hilbert space and a
representation of the translation group with natural properties, we construct
and analyze for each endomorphism of this pair a local, translationally
covariant net of standard subspaces, on the lightray and on two-dimensional
Minkowski space. These nets share many features with low-dimensional quantum
field theory, described by corresponding nets of von Neumann algebras.
Generalizing a result of Longo and Witten to two dimensions and massive
multiplicity free representations, we characterize these endomorphisms in terms
of specific analytic functions. Such a characterization then allows us to
analyze the corresponding nets of standard spaces, and in particular compute
their minimal localization length. The analogies and differences to the von
Neumann algebraic situation are discussed.Comment: 34 pages, 1 figur
Spectral Factorization of Rank-Deficient Rational Densities
Though there have been hundreds of methods on solving rational spectral
factorization, most of them are based on a positive definite density matrix
assumption. In this work, we propose a novel approach on the spectral
factorization of a low-rank spectral density, to a minimum-phase full-rank
factor. Compared with other several approaches on low-rank spectral
factorizations, our approach uses the deterministic relation inside a factor,
leading to a high computation efficiency. In addition, we shall show that this
method is easily used in identification of low-rank processes and Wiener
Filter.Comment: 25 page
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