Matches in SemOpenAlex for { <https://semopenalex.org/work/W3105431356> ?p ?o ?g. }
- W3105431356 endingPage "013003" @default.
- W3105431356 startingPage "013003" @default.
- W3105431356 abstract "In this paper, we show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a representation of the observable algebra including operators of quantum geometry. In particular, we consider the holonomy-flux algebra of (2 + 1)-dimensional Euclidean loop quantum gravity, and construct a new representation of this algebra that incorporates a positive cosmological constant. The vacuum state underlying our representation is defined by the Turaev–Viro TQFT. This vacuum state can be thought of as being peaked on connections with homogeneous curvature. We therefore construct here a generalization, or more precisely a quantum deformation at root of unity, of the previously introduced SU(2) BF representation. The extended Turaev–Viro TQFT provides a description of the excitations on top of the vacuum. These curvature and torsion excitations are classified by the Drinfeld center category of the quantum deformation of SU(2), and are essential in order to allow for a representation of the holonomies and fluxes. The holonomies and fluxes are generalized to ribbon operators which create and interact with the excitations. These excitations agree with the ones induced by massive and spinning particles, and therefore the framework presented here allows automatically for a description of the coupling of such matter to -dimensional gravity with a cosmological constant. The new representation constructed here presents a number of advantages over the representations which exist so far. In particular, it possesses a very useful finiteness property which guarantees the discreteness of spectra for a wide class of quantum (intrinsic and extrinsic) geometrical operators. Also, the notion of basic excitations leads to a so-called fusion basis which offers exciting possibilities for the construction of states with interesting global properties, as well as states with certain stability properties under coarse graining. In addition, the work presented here showcases how the framework of extended TQFTs, as well as techniques from condensed matter, can help design new representations, and construct and understand the associated notion of basic excitations. This is essential in order to find the best starting point for the construction of the dynamics of quantum gravity, and will enable the study of possible phases of spin foam models and group field theories from a new perspective." @default.
- W3105431356 created "2020-11-23" @default.
- W3105431356 creator A5017055505 @default.
- W3105431356 creator A5045729371 @default.
- W3105431356 date "2017-01-06" @default.
- W3105431356 modified "2023-10-01" @default.
- W3105431356 title "Quantum gravity kinematics from extended TQFTs" @default.
- W3105431356 cites W1491726941 @default.
- W3105431356 cites W1499008244 @default.
- W3105431356 cites W1531177993 @default.
- W3105431356 cites W1643540041 @default.
- W3105431356 cites W1947273351 @default.
- W3105431356 cites W1965001977 @default.
- W3105431356 cites W1966195009 @default.
- W3105431356 cites W1969178136 @default.
- W3105431356 cites W1969737000 @default.
- W3105431356 cites W1972018751 @default.
- W3105431356 cites W1976415611 @default.
- W3105431356 cites W1976604005 @default.
- W3105431356 cites W1978695735 @default.
- W3105431356 cites W1981610565 @default.
- W3105431356 cites W1994745108 @default.
- W3105431356 cites W1997750865 @default.
- W3105431356 cites W2003786459 @default.
- W3105431356 cites W2019558609 @default.
- W3105431356 cites W2022355630 @default.
- W3105431356 cites W2023113112 @default.
- W3105431356 cites W2037266697 @default.
- W3105431356 cites W2055144949 @default.
- W3105431356 cites W2067449039 @default.
- W3105431356 cites W2069482748 @default.
- W3105431356 cites W2070707213 @default.
- W3105431356 cites W2077485894 @default.
- W3105431356 cites W2078381478 @default.
- W3105431356 cites W2079781859 @default.
- W3105431356 cites W2083957217 @default.
- W3105431356 cites W2085084116 @default.
- W3105431356 cites W2091047536 @default.
- W3105431356 cites W2094673477 @default.
- W3105431356 cites W2098768551 @default.
- W3105431356 cites W2098989214 @default.
- W3105431356 cites W2106021864 @default.
- W3105431356 cites W2111432497 @default.
- W3105431356 cites W2111486899 @default.
- W3105431356 cites W2115210520 @default.
- W3105431356 cites W2116722231 @default.
- W3105431356 cites W2117195577 @default.
- W3105431356 cites W2124214065 @default.
- W3105431356 cites W2125333040 @default.
- W3105431356 cites W2126106103 @default.
- W3105431356 cites W2134209739 @default.
- W3105431356 cites W2135273380 @default.
- W3105431356 cites W2137409288 @default.
- W3105431356 cites W2138547238 @default.
- W3105431356 cites W2139401611 @default.
- W3105431356 cites W2144505517 @default.
- W3105431356 cites W2150700562 @default.
- W3105431356 cites W2155091916 @default.
- W3105431356 cites W2161026547 @default.
- W3105431356 cites W2171162942 @default.
- W3105431356 cites W2276514502 @default.
- W3105431356 cites W2343954838 @default.
- W3105431356 cites W2482487924 @default.
- W3105431356 cites W2963438085 @default.
- W3105431356 cites W2963782509 @default.
- W3105431356 cites W3098077061 @default.
- W3105431356 cites W3100362012 @default.
- W3105431356 cites W3100406328 @default.
- W3105431356 cites W3100673830 @default.
- W3105431356 cites W3101007789 @default.
- W3105431356 cites W3101438216 @default.
- W3105431356 cites W3102731393 @default.
- W3105431356 cites W3103729200 @default.
- W3105431356 cites W3104679310 @default.
- W3105431356 cites W3104756349 @default.
- W3105431356 cites W3104856735 @default.
- W3105431356 cites W3106024890 @default.
- W3105431356 cites W3124386867 @default.
- W3105431356 cites W4233500204 @default.
- W3105431356 cites W4238114872 @default.
- W3105431356 cites W4239309077 @default.
- W3105431356 doi "https://doi.org/10.1088/1367-2630/aa54e2" @default.
- W3105431356 hasPublicationYear "2017" @default.
- W3105431356 type Work @default.
- W3105431356 sameAs 3105431356 @default.
- W3105431356 citedByCount "41" @default.
- W3105431356 countsByYear W31054313562017 @default.
- W3105431356 countsByYear W31054313562018 @default.
- W3105431356 countsByYear W31054313562019 @default.
- W3105431356 countsByYear W31054313562020 @default.
- W3105431356 countsByYear W31054313562021 @default.
- W3105431356 countsByYear W31054313562022 @default.
- W3105431356 countsByYear W31054313562023 @default.
- W3105431356 crossrefType "journal-article" @default.
- W3105431356 hasAuthorship W3105431356A5017055505 @default.
- W3105431356 hasAuthorship W3105431356A5045729371 @default.
- W3105431356 hasBestOaLocation W31054313561 @default.
- W3105431356 hasConcept C108568745 @default.