On the diffeomorphism commutators of lattice quantum gravity

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.Comment: 16 pages, Te

Cultural Expertise and Socio-legal Studies: Introduction

International audienceEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services. Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation

Emergent diffeomorphism invariance in a discrete loop quantum gravity model

Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory becomes second class upon discretization. If one treats the second class constraints properly, the resulting theories have very different dynamics and number of degrees of freedom than those of the continuum theory. It is therefore questionable how these theories could be considered a starting point for quantization and the definition of a continuum theory through a continuum limit. We show explicitly in a model that the {\em uniform discretizations} approach to the quantization of constrained systems overcomes these difficulties. We consider here a simple diffeomorphism invariant one dimensional model and complete the quantization using {\em uniform discretizations}. The model can be viewed as a spherically symmetric reduction of the well known Husain--Kucha\v{r} model of diffeomorphism invariant theory. We show that the correct quantum continuum limit can be satisfactorily constructed for this model. This opens the possibility of treating 1+1 dimensional dynamical situations of great interest in quantum gravity taking into account the full dynamics of the theory and preserving the space-time covariance at a quantum level.Comment: 12 pages, Revte

The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity

The Hamiltonian constraint remains the major unsolved problem in Loop Quantum Gravity (LQG). Seven years ago a mathematically consistent candidate Hamiltonian constraint has been proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper we propose a solution to this set of problems based on the so-called {\bf Master Constraint} which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint. If certain mathematical conditions, which still have to be proved, hold, then not only the problems with the commutator algebra could disappear, also chances are good that one can control the solution space and the (quantum) Dirac observables of LQG. Even a decision on whether the theory has the correct classical limit and a connection with the path integral (or spin foam) formulation could be in reach. While these are exciting possibilities, we should warn the reader from the outset that, since the proposal is, to the best of our knowledge, completely new and has been barely tested in solvable models, there might be caveats which we are presently unaware of and render the whole {\bf Master Constraint Programme} obsolete. Thus, this paper should really be viewed as a proposal only, rather than a presentation of hard results, which however we intend to supply in future submissions.Comment: LATEX, uses AMSTE

Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion

Geriatric patients' expectations of their physicians: findings from a tertiary care hospital in Pakistan

<p>Abstract</p> <p>Background</p> <p>Geriatric health is a neglected and under-explored area internationally and in Pakistan. We aimed to ascertain the expectations of the geriatric patients from their physicians and the factors associated with patient satisfaction in this particular age bracket.</p> <p>Methods</p> <p>A cross-sectional survey was carried out at a tertiary care teaching hospital in Karachi, Pakistan. Data collection was carried out via face-to-face interviews based on structured, pre-tested questionnaires. All consenting individuals aged 65 years or above were recruited into the study. Convenience sampling was used to draw the sample. The data was analyzed using SPSS version 16. Geriatric patient's expectations from physicians were elicited using a set of 11 questions that were graded on a scale of 1-3 where 1 = not important, 2 = important, 3 = very important.</p> <p>Results</p> <p>Three hundred and eighty geriatric patients were interviewed. The response rate of this study was 89.8%. The mean age of the respondents was 73.4 ± 6.8 years. Two hundred and forty eight respondents (65.3%) were female. Diabetes mellitus (53.7%), hypertension (59.5%), arthritis (40.5%) and renal disease (32.1%) were common ailments among geriatric patients. More than 50% of the patients were visiting their physicians once every two to three months. Discussing treatment options and letting patients make the final decision (79.2%), prescribing minimum possible medications (84.5%), physician's holistic knowledge about the spectrum of care issues for geriatric patients (79.2%), being given a realistic but optimistic picture of future health by physicians (85.5%) were ranked as very important expectations by patients from their physicians. Cumulative household income (p = 0.005), most important health complaint (p = 0.01) and frequency of experiencing health complaint (p < 0.001) emerged as independent predictors of the satisfaction of geriatric patients from care provided by physicians.</p> <p>Conclusion</p> <p>We have documented the expectations of the geriatric patients from their physicians in a developing country. Physicians belonging to all disciplines should keep these expectations in mind during clinical encounters with geriatric patients.</p

Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity

We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar mechanism in the presence of pressure free dust fields which allows to deparametrise the theory and 2. Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gauge invariant observables. Since the resulting algebra of observables is very simple, one can quantise it using the methods of LQG. Basically, the kinematical Hilbert space of non reduced LQG now becomes a physical Hilbert space and the kinematical results of LQG such as discreteness of spectra of geometrical operators now have physical meaning. The constraints have disappeared, however, the dynamics of the observables is driven by a physical Hamiltonian which is related to the Hamiltonian of the standard model (without dust) and which we quantise in this paper.Comment: 31 pages, no figure