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The strings actually only exist in 3 dimensions as all the other dimensions, except maybe the 11th, are compactified. In 3-d they are all the material and light particles we know so well. That is, the strings become quarks, which make up protons and neutrons, electrons and photons. In short, the strings are everything in the world but space.
The 11th dimension connects two 10-d worlds. One world would be perhaps Dark Matter whereas the other is us.
In each world 6 of the 10 dimensions roll up into tiny, more or less Planck sized balls of very complicated shapes called manifolds at every 3-d point in space. The other dimension is time. We can only see one point on the time dimension. But we all see pretty much the same series of points if we are not relativistic. Photons which are relativistic exist at only one point in time.
The most difficult problem is superstring theory is how the 6-Ds are compactified. The strings vibrate in the compactified dimensions, but even this is not understood. But the vibrations are what distinguishes one particle from another.
The M stands for membrane. I do not understand how membranes fit into string theory. It seems that strings can be attached to membranes. BTW they are 2-d surfaces in the 3-d world. Those are called 2branes. But there are also 3branes and 4branes and 5branes, which are higher order surfaces in a 10-d world. It is again not known how branes compactify.
String theory and LQG are completely different theory. The Loops in LQG stand for Wilson loops, which is just a path integral around a loop. They are not strings embedded in a background space. The loops are "weaved" together to make space itself. There may be books and Scientific Am articles or New Scientist articles describing LQG, but I have not been to the library lately to know. I can give you the seminal paper where area was first derived from loops, which is more words than equations, written by the co-founders of LQG:
http://arXiv.org/abs/hep-th/9203079
But Rovelli and Smolin, once the young Turks under Ashtekar, have been replaced by others. Bojowald seems to be the best since he derived the big bang from LQG. Livine seems to be the next genius.
So I will give you references to all their work. They contain equations, but you like me can read around they equations to get a direct impression of what it's all about. I include Alexander as he first did string theory and then switched to LQG.
LQG is entirely done in 3-d plus time. That is, that is all they have derived so far. I hope that they eventually address higher dimensionality some day so as to connect to string theory.
To get an idea of what other physicists think of LQG and string theory, read some of the posts on the Physics Forum:
http://www.physicsforums.com/forumdisplay.php?s=&forumid=66
Here are the references:
Bojowald
In each case put hppt://arXiv.org/abs/ in front of the paper number tom get a link,i.e., for #1
hppt://arXiv.org/abs/astro-ph/0309478
Just cut & paste each part
1. astro-ph/0309478 [abs, ps, pdf, other] :
Title: Quantum Gravity and the Big Bang
Authors: Martin Bojowald
Comments: 6 pages, invited talk at the conference "Where Cosmology and Fundamental Physics Meet" at IUFM, Marseille, June 23 - 26, 2003
2. gr-qc/0307083 [abs, ps, pdf, other] :
Title: Consistency Conditions for Fundamentally Discrete Theories
Authors: Martin Bojowald, Ghanashyam Date
Comments: 33 pages
3. gr-qc/0306008 [abs, ps, pdf, other] :
Title: Cosmological applications of loop quantum gravity
Authors: Martin Bojowald, Hugo A. Morales-Tecotl
Comments: 42 pages, 4 figures, written for the proceedings of the Fifth Mexican School (DGFM): The Early Universe and Observational Cosmology
4. gr-qc/0305069 [abs, ps, pdf, other] :
Title: Initial Conditions for a Universe
Authors: Martin Bojowald
Comments: 7 pages, this essay was awarded First Prize in the Gravity Research Foundation Essay Contest 2003
5. hep-th/0304252 [abs, ps, pdf, other] :
Title: Classical Solutions for Poisson Sigma Models on a Riemann surface
Authors: Martin Bojowald, Thomas Strobl
Comments: 28 pages
Subj-class: High Energy Physics - Theory; Symplectic Geometry
Journal-ref: JHEP 0307 (2003) 002
6. gr-qc/0304074 [abs, ps, pdf, other] :
Title: Mathematical structure of loop quantum cosmology
Authors: Abhay Ashtekar, Martin Bojowald, Jerzy Lewandowski
Comments: 29 pages, v2: minor corrections, v3: remark added in appendix
Subj-class: General Relativity and Quantum Cosmology; Mathematical Physics
Journal-ref: Adv.Theor.Math.Phys. 7 (2003) 233-268
7. gr-qc/0303073 [abs, ps, pdf, other] :
Title: Homogeneous Loop Quantum Cosmology
Authors: Martin Bojowald
Comments: 25 pages, 3 figures
Journal-ref: Class.Quant.Grav. 20 (2003) 2595-2615
8. gr-qc/0303072 [abs, ps, pdf, other] :
Title: Loop Quantum Cosmology, Boundary Proposals, and Inflation
Authors: Martin Bojowald, Kevin Vandersloot
Comments: 20 pages, 6 figures
Journal-ref: Phys.Rev. D67 (2003) 124023
9. gr-qc/0303026 [abs, ps, pdf, other] :
Title: Spin Foam Quantization and Anomalies
Authors: Martin Bojowald, Alejandro Perez
Comments: 32 pages
10. gr-qc/0207038 [abs, ps, pdf, other] :
Title: Isotropic Loop Quantum Cosmology with Matter
Authors: Martin Bojowald, Franz Hinterleitner
Comments: 18 pages, 4 figures
Journal-ref: Phys.Rev. D66 (2002) 104003
11. gr-qc/0206054 [abs, ps, pdf, other] :
Title: Inflation from Quantum Geometry
Authors: Martin Bojowald
Comments: 4 pages, 3 figures
Journal-ref: Phys.Rev.Lett. 89 (2002) 261301
12. gr-qc/0206053 [abs, ps, pdf, other] :
Title: Quantization Ambiguities in Isotropic Quantum Geometry
Authors: Martin Bojowald
Comments: 20 pages, 6 figures
Journal-ref: Class.Quant.Grav. 19 (2002) 5113-5230
13. gr-qc/0202077 [abs, ps, pdf, other] :
Title: Isotropic Loop Quantum Cosmology
Authors: Martin Bojowald
Comments: 30 pages
Journal-ref: Class.Quant.Grav. 19 (2002) 2717-2742
14. hep-th/0112074 [abs, ps, pdf, other] :
Title: Poisson Geometry in Constrained Systems
Authors: Martin Bojowald, Thomas Strobl
Comments: 41 pages, more detailed abstract in paper; v2: minor corrections and an additional reference
Subj-class: High Energy Physics - Theory; Symplectic Geometry
15. gr-qc/0105113 [abs, ps, pdf, other] :
Title: The Semiclassical Limit of Loop Quantum Cosmology
Authors: Martin Bojowald
Comments: 10 pages
Journal-ref: Class.Quant.Grav. 18 (2001) L109-L116
16. gr-qc/0105067 [abs, ps, pdf, other] :
Title: The Inverse Scale Factor in Isotropic Quantum Geometry
Authors: Martin Bojowald
Comments: 17 pages, 4 figures
Journal-ref: Phys.Rev. D64 (2001) 084018
17. gr-qc/0104072 [abs, ps, pdf, other] :
Title: Dynamical Initial Conditions in Quantum Cosmology
Authors: Martin Bojowald
Comments: 4 pages, 1 figure
Journal-ref: Phys.Rev.Lett. 87 (2001) 121301
18. gr-qc/0102069 [abs, ps, pdf, other] :
Title: Absence of Singularity in Loop Quantum Cosmology
Authors: Martin Bojowald
Comments: 4 pages, 1 figure
Journal-ref: Phys.Rev.Lett. 86 (2001) 5227-5230
19. gr-qc/0101061 [abs, ps, pdf, other] :
Title: Symmetric States in Quantum Geometry
Authors: M. Bojowald, H. A. Kastrup
Comments: 9 pages, talk at the Ninth Marcel Grossmann Meeting, Rome, July 2-8, 2000
23. gr-qc/0008054 [abs, ps, pdf, other] :
Title: Angular Momentum in Loop Quantum Gravity
Authors: Martin Bojowald
Comments: 9 pages
24. gr-qc/0008053 [abs, ps, pdf, other] :
Title: Loop Quantum Cosmology IV: Discrete Time Evolution
Authors: Martin Bojowald
Comments: 21 pages
Journal-ref: Class.Quant.Grav. 18 (2001) 1071-1088
25. gr-qc/0008052 [abs, ps, pdf, other] :
Title: Loop Quantum Cosmology III: Wheeler-DeWitt Operators
Authors: Martin Bojowald
Comments: 19 pages
Journal-ref: Class.Quant.Grav. 18 (2001) 1055-1070
26. quant-ph/9912048 [abs, ps, pdf, other] :
Title: Symplectic Cuts and Projection Quantization
Authors: Martin Bojowald, Thomas Strobl
Comments: 12 pages, v2: additional examples and a new reference to related work
Subj-class: Quantum Physics; Symplectic Geometry
Journal-ref: Int.J.Mod.Phys. D12 (2003) 713-725
28. gr-qc/9910104 [abs, ps, pdf, other] :
Title: Loop Quantum Cosmology II: Volume Operators
Authors: Martin Bojowald
Comments: 21 pages
Journal-ref: Class.Quant.Grav. 17 (2000) 1509-1526
29. gr-qc/9910103 [abs, ps, pdf, other] :
Title: Loop Quantum Cosmology I: Kinematics
Authors: Martin Bojowald
Comments: 24 pages
Journal-ref: Class.Quant.Grav. 17 (2000) 1489-1508
30. hep-th/9908170 [abs, ps, pdf, other] :
Title: Abelian BF-Theory and Spherically Symmetric Electromagnetism
Authors: Martin Bojowald
Comments: 21 pages, LaTeX2e, v2: minor corrections in some formulas and a new reference
Journal-ref: J.Math.Phys. 41 (2000) 4313-4329
31. quant-ph/9908079 [abs, ps, pdf, other] :
Title: Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+
Authors: Martin Bojowald, Thomas Strobl
Comments: 41 pages, LaTeX2e
Journal-ref: J.Math.Phys. 41 (2000) 2537-2567
32. hep-th/9907043 [abs, ps, pdf, other] :
Title: The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
Authors: M. Bojowald, H.A. Kastrup (RWTH Aachen, Germany)
Comments: 16 pages, Latex
Journal-ref: Class.Quant.Grav. 17 (2000) 3009-3043
33. hep-th/9907042 [abs, ps, pdf, other] :
Title: Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
Authors: M. Bojowald, H.A. Kastrup (RWTH Aachen, Germany)
Comments: 43 pages, Latex
Journal-ref: Class.Quant.Grav. 17 (2000) 3009-3043
34. gr-qc/9906105 [abs, ps, pdf, other] :
Title: Group Theoretical Quantization of a Phase Space S^1 x R^+ and the Mass Spectrum of Schwarzschild Black Holes in D Space-Time Dimensions
Authors: M. Bojowald, H.A. Kastrup, F. Schramm, T. Strobl (RWTH Aachen, Germany)
Comments: 45 pages, Latex; version accepted for publication in Phys. Rev. D (Refs. added, small changes in the introduction, no changes of results)
Journal-ref: Phys.Rev. D62 (2000) 044026
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Etera R. Livine
1. gr-qc/0311032 [abs, ps, pdf, other] :
Title: Quantizing speeds with the cosmological constant
Authors: Florian Girelli, Etera R. Livine
Comments: 4 pages, revtex4, 3 figures
2. gr-qc/0309028 [abs, ps, pdf, other] :
Title: Boucles et Mousses de Spin en Gravite Quantique
Authors: Etera R. Livine
Comments: 165 pages, in French; PhD Thesis 2003, Centre de Physique Theorique CNRS-UPR 7061 (France)
3. hep-th/0307251 [abs, ps, pdf, other] :
Title: Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models
Authors: Etera R. Livine, Robert Oeckl
Comments: 43 pages, 10 figures
4. gr-qc/0302018 [abs, ps, pdf, other] :
Title: Causality in spin foam models for quantum gravity
Authors: Etera R. Livine, Daniele Oriti
Comments: 6 pages; uses IOP conference macros; to appear in the Proceedings of the 15th SIGRAV Conference on General Relativity and Gravitational Physics
5. gr-qc/0212077 [abs, ps, pdf, other] :
Title: Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
Authors: Laurent Freidel, Etera R. Livine, Carlo Rovelli
Comments: RevTex, 13 pages, v2: references added
Journal-ref: Class.Quant.Grav. 20 (2003) 1463-1478
6. hep-th/0212043 [abs, ps, pdf, other] :
Title: BRST quantization of Matrix Chern-Simons Theory
Authors: Etera R. Livine, Lee Smolin
Comments: Latex, 8 pages
7. gr-qc/0210064 [abs, ps, pdf, other] :
Title: Implementing causality in the spin foam quantum geometry
Authors: Etera R. Livine, Daniele Oriti
Comments: Latex,39 pages,8 figures, v3: minor changes, typos in some formulas corrected, comments added, discussion of results improved
Journal-ref: Nucl.Phys. B663 (2003) 231-279
DOI: 10.1016/S0550-3213(03)00378-X
8. gr-qc/0209105 [abs, ps, pdf, other] :
Title: SU(2) Loop Quantum Gravity seen from Covariant Theory
Authors: Sergei Alexandrov, Etera R. Livine
Comments: LaTeX, 21 pages
Journal-ref: Phys.Rev. D67 (2003) 044009
9. gr-qc/0207084 [abs, ps, pdf, other] :
Title: Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
Authors: Etera R Livine
Comments: Latex, 15 pages
Journal-ref: Class.Quant.Grav. 19 (2002) 5525-5542
10. hep-th/0205268 [abs, ps, pdf, other] :
Title: Spin Networks for Non-Compact Groups
Authors: Laurent Freidel (PI, ENS-Lyon), Etera R. Livine (CPT Marseille)
Comments: 43pages, many figures, some comments added
Journal-ref: J.Math.Phys. 44 (2003) 1322-1356
-------------------------------------
Alexander
1. hep-th/0309045 [abs, ps, pdf, other] :
Title: Quantum Gravity and Inflation
Authors: Stephon Alexander, Justin Malecki, Lee Smolin
Comments: 18 Pages, 2 Figures
2. hep-th/0302160 [abs, ps, pdf, other] :
Title: Non-Topological Inflation from Embedded Defects
Authors: Stephon Alexander (SLAC and Stanford ITP), Robert Brandenberger (Brown), Moshe Rozali (UBC)
Comments: A few references added
3. hep-th/0212151 [abs, ps, pdf, other] :
Title: Brane Gas Cosmology, M-theory and Little String Theory
Authors: Stephon H.S. Alexander
Comments: 8 pages
Journal-ref: JHEP 0310 (2003) 013
4. hep-th/0108190 [abs, ps, pdf, other] :
Title: Non-Commutative Inflation
Authors: Stephon Alexander, Robert Brandenberger, Joao Magueijo (Imperial College and Brown University)
Comments: 4 pages, 3 figures
Journal-ref: Phys.Rev. D67 (2003) 081301
5. hep-th/0106097 [abs, ps, pdf, other] :
Title: A thermal instability for positive brane cosmological constant in the Randall-Sundrum cosmologies
Authors: Stephon Alexander, Yi Ling, Lee Smolin
Comments: 14 pages. The discussion on the relation between temperature and effective 4d cosmological constant is changed. References are added
Journal-ref: Phys.Rev. D65 (2002) 083503
6. hep-th/0105032 [abs, ps, pdf, other] :
Title: Inflation from D-\bar{D} brane annihilation
Authors: Stephon H.S. Alexander
Comments: 8 pages, 2 figures
Journal-ref: Phys.Rev. D65 (2002) 023507
7. hep-th/0104093 [abs, ps, pdf, other] :
Title: Non-commutative geometry as a realization of varying speed of light cosmology
Authors: Stephon H.S. Alexander, Joćo Magueijo
Comments: 11 pages, 7 figures
8. hep-th/0005212 [abs, ps, pdf, other] :
Title: Brane Gases in the Early Universe
Authors: S. Alexander, R. Brandenberger, D. Easson (Brown Univ.)
Comments: 8 pages, 1 figure; typos corrected; published in PRD
Journal-ref: Phys.Rev. D62 (2000) 103509
9. hep-th/9912037 [abs, ps, pdf, other] :
Title: On The Varying Speed of Light in a Brane-Induced FRW Universe
Authors: Stephon H.S. Alexander
Comments: 6 Pages Revised Version: Additional references included. Circular Geodesic found for speed of light stabilization
Journal-ref: JHEP 0011 (2000) 017
10. hep-ph/9903254 [abs, ps, pdf, other] :
Title: On the Interaction of Monopoles and Domain Walls
Authors: Stephon Alexander, Robert Brandenberger, Richard Easther, Andrew Sornborger
Comments: Preprint version contains "low resolution" figures to reduce the size of overall postscript file. Please contact authors to obtain the high resolution version
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