2,683 research outputs found
Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple
Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with
the group SU(2) in this manner. They are useful for regularizing quantum field
theories and modeling spacetimes by non-commutative manifolds. We show that
fuzzy spaces are Hopf algebras and in fact have more structure than the latter.
They are thus candidates for quantum symmetries. Using their generalized Hopf
algebraic structures, we can also model processes where one fuzzy space splits
into several fuzzy spaces. For example we can discuss the quantum transition
where the fuzzy sphere for angular momentum J splits into fuzzy spheres for
angular momenta K and L.Comment: LaTeX, 13 pages, v3: minor additions, added references, v4: corrected
typos, to appear in IJMP
Fuzzy Authentication using Rank Distance
Fuzzy authentication allows authentication based on the fuzzy matching of two
objects, for example based on the similarity of two strings in the Hamming
metric, or on the similiarity of two sets in the set difference metric. Aim of
this paper is to show other models and algorithms of secure fuzzy
authentication, which can be performed using the rank metric. A few schemes are
presented which can then be applied in different scenarios and applications.Comment: to appear in Cryptography and Physical Layer Security, Lecture Notes
in Electrical Engineering, Springe
Hopf algebras for matroids over hyperfields
Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids. In this paper we generalize the notion of minors and direct sums from ordinary matroids to matroids over hyperfields. Using this we generalize the classical construction of matroid-minor Hopf algebras to the case of matroids over hyperfields
Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz
We study the dimensional aspect of the geometry of quantum spaces.
Introducing a physically motivated notion of the scaling dimension, we study in
detail the model based on a fuzzy torus. We show that for a natural choice of a
deformed Laplace operator, this model demonstrates quite non-trivial behaviour:
the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with
the similar property, the so-called Horava-Lifshitz model, our construction
does not have any preferred direction. The dimension flow is rather achieved by
a rearrangement of the degrees of freedom. In this respect the number of
dimensions is deceptive. Some physical consequences are discussed.Comment: 20 pages + extensive appendix. 3 figure
Angles in Fuzzy Disc and Angular Noncommutative Solitons
The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region
in a noncommutative plane, and is a fuzzy approximation of a commutative disc.
In this paper we show that one can introduce a concept of angles to the fuzzy
disc, by using the phase operator and phase states known in quantum optics. We
gave a description of a fuzzy disc in terms of operators and their commutation
relations, and studied properties of angular projection operators. A similar
construction for a fuzzy annulus is also given. As an application, we
constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy
disc, which corresponds to a fan-shaped D-brane. We also applied this concept
to the theory of noncommutative gravity that we proposed in Ref.[2]. In
addition, possible connections to black hole microstates, holography and an
experimental test of noncommutativity by laser physics are suggested.Comment: 24 pages, 12 figures; v2: minor mistake corrected in Eq.(3.21), and
discussion adapted accordingly; v3: a further discussion on the algebra of
the fuzzy disc added in subsection 3.2; v4: discussions improved and typos
correcte
- …