QUANTUM TOPOLOGY CHANGE IN (2+1)d

Balachandran, A. P.; Batista, Eliezer; Silva, I. P. Costa e; Teotonio-Sobrinho, P.

doi:10.1142/s0217751x00000732

Cited by 11 publications

(21 citation statements)

References 35 publications

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“…This model has the advantage of "isolating" the topological degrees of freedom, which are in a certain sense canonically quantized independently from degrees of freedom coming from metric and other fields. The same model has been considered in a companion paper [6], and there we show that we may consider topology change as a quantum phenomenon depending on the scale of observations. Therefore this model features spatial topology change in some sense.…”

Section: Introductionmentioning

confidence: 71%

“…Here, the spatial manifold Σ is two-dimensional, and will be typically assumed to be a plane with one or several handles. Topological geons in this (2 + 1)d context are simply (for orientable space-times) these handles on the spatial manifold (for a more detailed account and a more general definition of geons see, for instance, [1,6,19]). Our aim in this section is to define some "observables" which describe the topological character of a geon.…”

Section: The Algebras For (+ 1)d Topological Geonsmentioning

confidence: 99%

“…Therefore the low-energy theory somehow actually allows for "topology fluctuations" of Σ as long as we stay within its limits. Such a way of viewing topology change is explored in [6]. It is very much akin to the views pursued in non-commutative geometry, where one uses an algebra to encode space-time geometry and topology.…”

Section: )mentioning

confidence: 99%

“…We will briefly outline here the main constructions. For details, see [6]. We recall that for a single geon, A (1) consists of three sub-algebras, generated by the "position observables" F (T ), the H-transformations C(H), and the "translations" , i.e., a realization M of the mapping class group M Σ .…”

Section: )mentioning

confidence: 99%

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The spin-statistics connection in quantum gravity

Balachandran¹,

Batista²,

Silva³

et al. 2000

Nuclear Physics B

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It is well-known that in spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of "observables" is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian "charge" and "magnetic flux". We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also discuss how our approach fits into conventional formulations of quantum gravity.

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Section: Introductionmentioning

confidence: 71%

Section: The Algebras For (+ 1)d Topological Geonsmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

See 2 more Smart Citations

The spin-statistics connection in quantum gravity

Balachandran¹,

Batista²,

Silva³

et al. 2000

Nuclear Physics B

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“…(2) It has turned up in string physics as quantized D-branes. (3) Certain approaches to canonical gravity [2] have also used noncommutative geometry with great effectiveness.…”

Section: Space-time In Quantum Physicsmentioning

confidence: 99%

Quantum space-times in the year 2002

Balachandran¹

2002

Pramana - J Phys

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We review certain emergent notions on the nature of space-time from noncommutative geometry and their radical implications. These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We find models of quantum space-time like fuzzy S 4 on which states cannot be localized, but which fluctuate into other manifolds like CP 3 . New uncertainty principles concerning such lack of localizability on quantum space-times are formulated. Such investigations show the possibility of formulating and answering questions like the probability of finding a point of a quantum manifold in a state localized on another one. Additional striking possibilities indicated by these developments is the (generic) failure of CPT 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. Space-time in quantum physicsThe point of departure from classical to quantum physics is the algebra ´Ì £ Éµ of functions on the classical phase space T £ Q. According to Dirac, quantization can be achieved by replacing a function f in this algebra by an operatorf and equating i times the Poisson bracket between functions to the commutator between the corresponding operators.In classical physics, the functions f commute, so ´Ì £ Éµ is a commutative algebra.But the corresponding quantum algebraˆ is not commutative. Dynamics is onˆ . So quantum physics is a noncommutative dynamics.A particular aspect of this dynamics is fuzzy phase space where we cannot localize points, and which has an attendent effective ultraviolet cut-off: The number of states in a phase space volume V is infinite in classical physics and V 2d in quantum physics when the phase space is of dimension 2d. The emergence of this cut-off from quantization is of particular importance for the program of fuzzy physics [1].This brings us to the focus of our talk. In quantum physics, the commutative algebra of functions on phase space is deformed to a noncommutative algebra, leading to a 'noncommutative phase space'. Such deformations, characteristic of quantum theory, are now appearing in different approaches to fundamental physics. The talk will focus on a few such selected approaches and their implications. 359

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Exact discreteness and mass gap of N = 1 symplectic Yang‐Mills from M‐theory

Boulton¹,

Moral

Restuccia

2007

Fortschritte der Physik

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In this note we summarize some of the results found recently in [1]. We show the pure discreteness of the non‐perturbative quantum spectrum of a symplectic Yang‐Mills theory defined on a Riemann surface of positive genus, living in a target space that, in particular, can be 4D. This theory corresponds to the membrane with central charges. The presence of the central charge induces a confinement in the phase at zero temperature. When the energy rises, the center of the group breaks and the theory enters in a quark‐plasma phase after a topological transition, corresponding to the N = 4 wrapped supermembrane.

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QUANTUM TOPOLOGY CHANGE IN (2+1)d

Cited by 11 publications

References 35 publications

The spin-statistics connection in quantum gravity

The spin-statistics connection in quantum gravity

Quantum space-times in the year 2002

Exact discreteness and mass gap of N = 1 symplectic Yang‐Mills from M‐theory

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