1,099 research outputs found
Quantum Spacetimes in the Year 1
We review certain emergent notions on the nature of spacetime from
noncommutative geometry and their radical implications. These ideas of
spacetime are suggested from developments in fuzzy physics, string theory, and
deformation quantisation. The review focuses on the ideas coming from fuzzy
physics. We find models of quantum spacetime like fuzzy on which states
cannot be localised, but which fluctuate into other manifolds like .
New uncertainty principles concerning such lack of localisability on quantum
spacetimes are formulated.Such investigations show the possibility of
formulating and answering questions like the probabilty of finding a point of a
quantum manifold in a state localised on another one. Additional striking
possibilities indicated by these developments is the (generic) failure of
theorem and the conventional spin-statistics connection. They even suggest that
Planck's `` constant '' may not be a constant, but an operator which does not
commute with all observables. All these novel possibilities arise within the
rules of conventional quantum physics,and with no serious input from gravity
physics.Comment: 11 pages, LaTeX; talks given at Utica and Kolkata .Minor corrections
made and references adde
Dual attachment pairs in categorically-algebraic topology
[EN] The paper is a continuation of our study on developing a new approach to (lattice-valued) topological structures, which relies on category theory and universal algebra, and which is called categorically-algebraic (catalg) topology. The new framework is used to build a topological setting, based in a catalg extension of the set-theoretic membership relation "e" called dual attachment, thereby dualizing the notion of attachment introduced by the authors earlier. Following the recent interest of the fuzzy community in topological systems of S. Vickers, we clarify completely relationships between these structures and (dual) attachment, showing that unlike the former, the latter have no inherent topology, but are capable of providing a natural transformation between two topological theories. We also outline a more general setting for developing the attachment theory, motivated by the concept of (L,M)-fuzzy topological space of T. Kubiak and A. Sostak.This research was partially supported by the ESF Project of the University of Latvia No. 2009/0223/1DP/1.1.1.2.0/09/APIA/VIAA/008.Frascella, A.; Guido, C.; Solovyov, SA. (2011). Dual attachment pairs in categorically-algebraic topology. Applied General Topology. 12(2):101-134. doi:10.4995/agt.2011.1646.SWORD10113412
Topology at the Planck Length
A basic arbitrariness in the determination of the topology of a manifold at
the Planck length is discussed. An explicit example is given of a `smooth'
change in topology from the 2-sphere to the 2-torus through a sequence of
noncommuting geometries. Applications are considered to the theory of D-branes
within the context of the proposed (atrix) theory.Comment: Orsay Preprint 97/34, 17 pages, Late
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