55,998 research outputs found

    Semiclassical quantization of gravity I: Entropy of horizons and the area spectrum

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    The principle of equivalence provides a description of gravity in terms of the metric tensor and determines how gravity affects the light cone structure of the space-time. This, in turn, leads to the existence of observers (in any space-time) who do not have access to regions of space-time bounded by horizons. To take into account this generic possibility, it is necessary to demand that \emph{physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access}. This principle is powerful enough to obtain the following results: (a) The action principle of gravity must be of such a structure that, in the semiclassical limit, the action of the unobserved degrees of freedom reduces to a boundary contribution AboundaryA_{\rm boundary} obtained by integrating a four divergence. (b) When the boundary is a horizon, AboundaryA_{\rm boundary} essentially reduces to a single, well-defined, term. (c) This boundary term must have a quantized spectrum with uniform spacing, ΔAboundary=2π\Delta A_{boundary}=2\pi\hbar, in the semiclassical limit. Using this principle in conjunction with the usual action principle in gravity, we show that: (i) The area of any one-way membrane is quantized. (ii) The information hidden by a one-way membrane leads to an entropy which is always one-fourth of the area of the membrane, in the leading order. (iii) In static space-times, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics.Comment: REvTex4, 19 page

    Role of Horizons in Semiclassical Gravity: Entropy and the Area Spectrum

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    In any space-time, it is possible to have a family of observers who have access to only part of the space-time manifold, because of the existence of a horizon. We demand that \emph{physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access}. In the coordinate frame in which these observers are at rest, the horizon manifests itself as a (coordinate) singularity in the metric tensor. Regularization of this singularity removes the inaccessible region, and leads to the following consequences: (a) The non-trivial topological structure for the effective manifold allows one to obtain the standard results of quantum field theory in curved space-time. (b) In case of gravity, this principle requires that the effect of the unobserved degrees of freedom should reduce to a boundary contribution AboundaryA_{\rm boundary} to the gravitational action. When the boundary is a horizon, AboundaryA_{\rm boundary} reduces to a single, well-defined term proportional to the area of the horizon. Using the form of this boundary term, it is possible to obtain the full gravitational action in the semiclassical limit. (c) This boundary term must have a quantized spectrum with uniform spacing, ΔAboundary=2π\Delta A_{boundary}=2\pi\hbar, in the semiclassical limit. This, in turn, yields the following results for semiclassical gravity: (i) The area of any one-way membrane is quantized. (ii) The information hidden by a one-way membrane amounts to an entropy, which is always one-fourth of the area of the membrane in the leading order. (iii) In static space-times, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics.Comment: Extends and presents the results of hep-th/0305165 in a broader context; clarifies some conceptual issues; 24 pages; revte

    A Transverse Lattice QCD Model for Mesons

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    QCD is analysed with two light-front continuum dimensions and two transverse lattice dimensions. In the limit of large number of colours and strong transverse gauge coupling, the contributions of light-front and transverse directions factorise in the dynamics, and the theory can be analytically solved in a closed form. An integral equation is obtained, describing the properties of mesons, which generalises the 't Hooft equation by including spin degrees of freedom. The meson spectrum, light-front wavefunctions and form factors can be obtained by solving this equation numerically. These results would be a good starting point to model QCD observables which only weakly depend on transverse directions, e.g. deep inelastic scattering structure functions.Comment: Lattice 2003 (theory), 3 page

    Measuring brand image: Shopping centre case studies

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    'Branding' is well known for consumer products but power has shifted from manufacturers' brands towards retailers'. The term 'image' is more common than 'brand' in the context of shopping centres, but 'branding' may become more important. In this study, the authors first investigated qualitatively, asking shoppers to describe centres in 'personality' terms and eliciting clear descriptive differences between centres. For example, one in-town centre was 'dull, boring and old-fashioned . . . not exciting, just OK'; a larger regional centre was 'trendy, prestigious . . . strong, vibrant, big and colourful'. Second, the authors evaluated six UK shopping centres quantitatively using a questionnaire survey (n = 287). The 'strong and vibrant' centre scored significantly higher than the 'dull and boring' one. Despite 'branding' being little used by shopping centres, those with the better 'brand images' tended to have larger catchment areas, sales and rental incomes. The authors contend that brand management could pay rewards in terms of customer numbers, sales turnover and rental income
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