QuantumGravityPrograms 2008-09-28 18:00:08 2008-09-28 18:00:08 Topic quantum gravity research programs % this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \subsection{Quantum Gravity programs} There are several distinct programs aimed at developing a Quantum Gravity theory. These include--but are not limited to-- the following. \begin{itemize} \item $\bullet$ The Penrose, twistors programme applied to an open curved space-time (ref. \cite{Hawking and Penrose}), (which is presumably a globally hyperbolic, relativistic space-time). This may also include the idea of developing a \emph{`sheaf cohomology'} for twistors (ref. \cite {Hawking and Penrose}) but still needs to justify the assumption in this approach of a charged, fundamental fermion of spin-3/2 of undefined mass and unitary `homogeneity' (which has not been observed so far); \item $\bullet$ The Weinberg, \emph{supergravity} theory, which is consistent with supersymmetry and superalgebra, and utilizes \emph{graded Lie algebras} and \emph{matter-coupled superfields} in the presence of \emph{weak} gravitational fields; \item $\bullet$ The programs of Hawking and Penrose \cite {Hawking and Penrose}) in quantum cosmology, concerned with singularities, such as black and `white' holes; S. W. Hawking combines, joins, or `glues' an initially flat Euclidean metric with convex Lorentzian metrics in the expanding, and then contracting, space-times with a very small value of Einstein's cosmological `constant'. Such `Hawking', double-pear shaped, space-times also have an initial Weyl tensor value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our universe, presumed to determine the irreversible arrow of time; furthermore, an observer will always be able to access through measurements only \emph{a limited part} of the global space-times in our universe; \item $\bullet$ The TQFT/HQFT approach that aims at finding the `topological' invariants of a manifold embedded in an abstract vector space related to the statistical mechanics problem of defining extensions of the partition function for many-particle quantum systems; \item $\bullet$ The string and superstring theories/M-theory that `live' in higher dimensional spaces (e.g., $n\geq 6$, preferred $n-dim =11$), and can be considered to be topological representations of physical entities that vibrate, are quantized, interact, and that might also be able to 'predict' fundamental masses relevant to quantum 'particles'; \item $\bullet$ The Baez `categorification' programme (\cite{Baez1}, \cite{Baez2}) that aims to deal with Quantum Field and QG problems at the abstract level of categories and functors in what seems to be mostly a global approach; \item $\bullet$ The `monoidal category' and valuation approach initiated by Isham (ref. \cite{Isham1}) to the quantum measurement problem and its possible solution through local-to-global, finite constructions in small categories. \end{itemize}