%%% This file is part of PlanetPhysics snapshot of 2011-09-01
%%% Primary Title: quantum gravity programs
%%% Primary Category Code: 04.60.-m
%%% Filename: QuantumGravityPrograms2.tex
%%% Version: 1
%%% Owner: bci1
%%% Author(s): bci1
%%% PlanetPhysics is released under the GNU Free Documentation License.
%%% You should have received a file called fdl.txt along with this file.
%%% If not, please write to gnu@gnu.org.
\documentclass[12pt]{article}
\pagestyle{empty}
\setlength{\paperwidth}{8.5in}
\setlength{\paperheight}{11in}
\setlength{\topmargin}{0.00in}
\setlength{\headsep}{0.00in}
\setlength{\headheight}{0.00in}
\setlength{\evensidemargin}{0.00in}
\setlength{\oddsidemargin}{0.00in}
\setlength{\textwidth}{6.5in}
\setlength{\textheight}{9.00in}
\setlength{\voffset}{0.00in}
\setlength{\hoffset}{0.00in}
\setlength{\marginparwidth}{0.00in}
\setlength{\marginparsep}{0.00in}
\setlength{\parindent}{0.00in}
\setlength{\parskip}{0.15in}
\usepackage{html}
% this is the default PlanetPhysics preamble.
% 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
\begin{document}
\subsection{Quantum Gravity Programs}
There are several distinct \htmladdnormallink{programs}{http://planetphysics.us/encyclopedia/SupercomputerArchitercture.html} aimed at developing a \htmladdnormallink{quantum gravity theory}{http://planetphysics.us/encyclopedia/SpaceTimeQuantizationInQuantumGravityTheories.html}. These include--but are not limited to-- the following.
\begin{itemize}
\item $\bullet$ The Penrose, twistors programme applied to an open curved \htmladdnormallink{space-time}{http://planetphysics.us/encyclopedia/SR.html} (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 \htmladdnormallink{fermion}{http://planetphysics.us/encyclopedia/AntiCommutationRelations.html} of spin-3/2 of undefined \htmladdnormallink{mass}{http://planetphysics.us/encyclopedia/Mass.html} and unitary `homogeneity' (which has not been observed so far);
\item $\bullet$ The Weinberg, \emph{\htmladdnormallink{supergravity}{http://planetphysics.us/encyclopedia/AntiCommutationRelations.html}} theory, which is consistent with \htmladdnormallink{supersymmetry}{http://planetphysics.us/encyclopedia/AntiCommutationRelations.html} and \htmladdnormallink{superalgebra}{http://planetphysics.us/encyclopedia/MathematicalFoundationsOfQuantumTheories.html}, and utilizes \emph{graded \htmladdnormallink{Lie algebras}{http://planetphysics.us/encyclopedia/BilinearMap.html}} and \emph{matter-coupled \htmladdnormallink{superfields}{http://planetphysics.us/encyclopedia/HamiltonianAlgebroid3.html}} in the presence of \emph{weak} gravitational \htmladdnormallink{fields}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html};
\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 \htmladdnormallink{metric}{http://planetphysics.us/encyclopedia/MetricTensor.html} with convex \htmladdnormallink{Lorentzian}{http://planetphysics.us/encyclopedia/LebesgueMeasure.html} metrics in the expanding, and then contracting, space-times with a very small value of \htmladdnormallink{Einstein's}{http://planetphysics.us/encyclopedia/AlbertEinstein.html} \htmladdnormallink{cosmological `constant}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}'. Such `Hawking', double-pear shaped, space-times also have an initial Weyl \htmladdnormallink{tensor}{http://planetphysics.us/encyclopedia/Tensor.html} value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our \htmladdnormallink{Universe}{http://planetphysics.us/encyclopedia/MultiVerses.html}, 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 \htmladdnormallink{TQFT/}{http://planetphysics.us/encyclopedia/NonAbelianQuantumAlgebraicTopology3.html} approach that aims at finding the `\htmladdnormallink{topological' invariants}{http://planetphysics.us/encyclopedia/ModuleAlgebraic.html} of a \htmladdnormallink{manifold}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry4.html} embedded in an abstract \htmladdnormallink{vector space}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html} related to the \htmladdnormallink{statistical mechanics}{http://planetphysics.us/encyclopedia/ThermodynamicLaws.html} problem of defining extensions of the partition \htmladdnormallink{function}{http://planetphysics.us/encyclopedia/Bijective.html} for many-particle quantum \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html};
\item $\bullet$ The string and \htmladdnormallink{superstring}{http://planetphysics.us/encyclopedia/10DBrane.html} theories/M-theory that `live' in higher dimensional spaces (e.g., $n\geq 6$, preferred $n-dim =11$), and can be considered to be \htmladdnormallink{topological}{http://planetphysics.us/encyclopedia/CoIntersections.html} \htmladdnormallink{representations}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of physical entities that
vibrate, are quantized, interact, and that might also be able to 'predict' fundamental masses relevant to \htmladdnormallink{quantum 'particles';}{http://planetphysics.us/encyclopedia/QuantumParticle.html}
\item $\bullet$ The Baez `\htmladdnormallink{categorification}{http://planetphysics.us/encyclopedia/Cod.html}' programme (\cite{Baez1}, \cite{Baez2}) that aims to deal with \htmladdnormallink{quantum field}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} and \htmladdnormallink{QG}{http://planetphysics.us/encyclopedia/SUSY2.html} problems at the abstract level of \htmladdnormallink{categories}{http://planetphysics.us/encyclopedia/Cod.html} and \htmladdnormallink{functors}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} 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 \htmladdnormallink{quantum measurement}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} problem and its possible solution through local-to-global, finite constructions in \htmladdnormallink{small categories}{http://planetphysics.us/encyclopedia/SmallCategory.html}.
\end{itemize}
Most of the quantum gravity programs are consistent with the Big-Bang theory,
or the theory of a rapidly \htmladdnormallink{expanding universe}{http://planetphysics.us/encyclopedia/ExpandingUniverse.html}, although none `prove' the necessity of its existence. Several competing and conflicting theories were
reported that deal with singularities in spacetime, such as \htmladdnormallink{black holes}{http://planetphysics.us/encyclopedia/BlackHoles.html} `without hair', evaporating black holes and naked singularities.
\begin{thebibliography}{99}
\bibitem{Baez1}
J. Baez. 2004. Quantum quandaries : a category theory perspective, in \emph{Structural Foundations of Quantum Gravity}, (ed. S. French et al.) Oxford Univ. Press.
\bibitem{Baez2}
J. Baez. 2002. Categorified Gauge Theory. in Proceedings of the Pacific Northwest Geometry Seminar Cascade Topology Seminar,Spring Meeting--May 11 and 12, 2002. University of Washington, Seattle, WA.
\bibitem{BGGB05}
I.C. Baianu, James Glazebrook, G. Georgescu and Ronald Brown. 2008.``Generalized `Topos' Representations of Quantum Space--Time: Linking Quantum $N$--Valued Logics with Categories and Higher Dimensional Algebra.'', (\emph{Preprint})
\bibitem{BIsham2}
J. Butterfield and C. J. Isham : A topos perspective on the Kochen--Specker theorem I - IV, \emph{Int. J. Theor. Phys},
\textbf{37} (1998) No 11., 2669--2733 \textbf{38} (1999) No 3.,
827--859, \textbf{39} (2000) No 6., 1413--1436, \textbf{41} (2002)
No 4., 613--639.
\bibitem{BIsham1}
J. Butterfield and C. J. Isham : Some possible roles for topos theory in quantum theory and quantum gravity, \emph{Foundations of Physics}.
\bibitem{FernCastro}
F.M. Fernandez and E. A. Castro. 1996. (Lie) \emph{Algebraic Methods in Quantum Chemistry and Physics.}, Boca Raton: CRC Press, Inc.
\bibitem{Feynman}
Feynman, R. P., 1948, ``Space--Time Approach to Non--Relativistic Quantum Mechanics'', \emph{Reviews of Modern Physics}, 20: 367--387. [It is reprinted in (Schwinger 1958).]
\bibitem{Hawking and Penrose}
S. W. Hawking and R. Penrose. 2000. \emph{The Nature of Space and Time}. Princeton and Oxford: Princeton University Press.
\bibitem{PLR}
R. J. Plymen and P. L. Robinson: Spinors in Hilbert Space.
\emph{Cambridge Tracts in Math.} \textbf{114}, \emph{Cambridge
Univ. Press} 1994.
\bibitem{Raptis2k}
I. Raptis : Algebraic quantisation of causal sets, \emph{Int.
Jour. Theor. Phys.} \textbf{39} (2000), 1233.
\bibitem{Raptis2}
I. Raptis : Quantum space-time as a quantum causal set,
$arXiv:gr-qc/0201004$.
\bibitem{noncomm}
J. E. Roberts : More lectures on algebraic quantum field theory
(in A. Connes, et al. (\emph{Non--commutative Geometry}), Springer (2004).
\bibitem{Rovelli}
C. Rovelli : Loop quantum gravity (1997), $arXiv:gr--qc/9710008$.
\bibitem{Smit}
Jan Smit. 2002. \emph{Quantum Field Theory on a Lattice}.
\bibitem{Weinberg}
S. Weinberg.1995--2000. \emph{The Quantum Theory of Fields}. Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3.
\bibitem{Wess-Bagger}
Wess and Bagger. 2000. Supergravity. (Weinberg)
\end{thebibliography}
\end{document}
