M-Theory and Quantum Geometry -

M-Theory and Quantum Geometry

Buch | Softcover
454 Seiten
2000 | Softcover reprint of the original 1st ed. 2000
Springer (Verlag)
978-0-7923-6475-7 (ISBN)
160,49 inkl. MwSt
The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge­ ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par­ ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but in recent years the focus has shifted to include also higher-dimensional ob­ jects, so called D-branes, which play a key role in the non-perturbative dynamics of the theory. A related development has seen the strong coupling regime of a given string theory identified with the weak coupling regime of what was previ­ ously believed to be a different theory, and a web of such" dualities" that interrelates all known superstring theories has emerged. The resulting uni­ fied theoretical framework, termed M-theory, has evolved at a rapid pace in recent years.

1 D Branes in String Theory, I.- 1 Introduction.- 2 Perturbative String Theory.- 3 Conformal Field Theory Formulation.- 4 T-Duality.- 5 Classical Solutions of The Low-Energy String Effective Action.- 6 Bosonic Boundary State.- 7 Fermionic Boundary State.- 8 Classical Solutions From Boundary State.- 9 Interaction Between a p and a p’ Brane.- 2 Moduli Spaces of Calabi-Yau Compactifications.- 1 Introduction.- 2 A short story about string theory, F-theory and M-theory.- 3 The q = 16 triplet.- 4 The q = 8 triplets.- A Calabi-Yau manifolds.- 3 The M(Atrix) Model of M-Theory.- 1 Introduction.- 2 Matrix theory from the quantized supermembrane.- 3 The BFSS conjecture.- 4 M-theory objects from matrix theory.- 5 Interactions in matrix theory.- 6 Matrix theory in a general background.- 7 Outlook.- 4 The Holographic Principle.- 1 Black Hole Complementarity.- 2 Entropy Bounds.- 3 The AdS/CFT Correspondence and the Holographic Principle.- 4 The Flat Space Limit.- 5 Born-Infeld Actions and D-Brane Physics.- 1 D-Brane Solitons and the Born-Infeld Action.- 2 Born-Infeld Dynamics of Branes in Flat Space.- 3 Branes in Curved Space and the Gauge Theory Connection.- 4 Born-Infeld Analysis of the Baryon Vertex.- 5 Applications of the AdS/CFT Correspondence.- 6 Summary.- 6 Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces.- 1 Introduction.- 2 A Simple Example of Conformal Quantum Mechanics.- 3 Conformally Invariant N-Particle Quantum Mechanics.- 4 Superconformal Quantum Mechanics.- 5 The Quantum Mechanics of a Test Particle in a Reissner-Nordström Background.- 6 Quantum Mechanics on the Black Hole Moduli Space.- 7 Discussion.- A Differential Geometry with Torsion.- 7 Large-N Gauge Theories.- 1 Introduction.- 2 0(N) Vector Models.- 3 Large-N QCD.- 4 QCD in LoopSpace.- 5 Large-N Reduction.- 8 Introduction to Random Surfaces.- 1 Introduction.- 2 Random paths.- 3 Branched polymers.- 4 Dynamicaly triangulated surfaces.- 5 Lattice surfaces.- 6 Conclusion.- 9 Lorentzian and Euclidean Quantum Gravity ¡ª Analytical and Numerical Results.- 1 Introduction.- 2 Lorentzian gravity in 2d.- 3 Topology changes and Euclidean quantum gravity.- 4 Euclidean quantum gravity.- 5 Numerical setup.- 6 Dynamically triangulated quantum gravity in d > 2.- 7 Outlook.

Reihe/Serie NATO Science Series C ; 556
Zusatzinfo XVIII, 454 p.
Verlagsort Dordrecht
Sprache englisch
Maße 160 x 240 mm
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Atom- / Kern- / Molekularphysik
Naturwissenschaften Physik / Astronomie Hochenergiephysik / Teilchenphysik
Naturwissenschaften Physik / Astronomie Quantenphysik
Naturwissenschaften Physik / Astronomie Theoretische Physik
ISBN-10 0-7923-6475-9 / 0792364759
ISBN-13 978-0-7923-6475-7 / 9780792364757
Zustand Neuware
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