超弦和M理论导论

Preface
Acknowledgments
Ⅰ First Quantization and Path Integrals
1 Path Integrals and Point Particles
1.1 Why Strings?
1.2 Historical Review of Gauge Theory
1.3 Path Integrals and Point Particles
1.4 Relativistic Point Particles
1.5 First and Second Quantization
1.6 Faddeev-Popov Quantization
1.7 Second Quantization
1.8 Harmonic Oscillators
1.9 Currents and Second Quantization
1.10 Summary
ReferencesPreface
Acknowledgments
Ⅰ First Quantization and Path Integrals
1 Path Integrals and Point Particles
1.1 Why Strings?
1.2 Historical Review of Gauge Theory
1.3 Path Integrals and Point Particles
1.4 Relativistic Point Particles
1.5 First and Second Quantization
1.6 Faddeev-Popov Quantization
1.7 Second Quantization
1.8 Harmonic Oscillators
1.9 Currents and Second Quantization
1.10 Summary
References

2 Nambu-Goto Strings
2.1 Bosonic Strings
2.2 Gupta-Bleuler Quantization
2.3 Light Cone Quantization
2.4 BRST Quantization
2.5 Trees
2.6 From Path Integrals to Operators
2.7 Projective Invariance and Twists
2.8 Closed Strings
2.9 Ghost Elimination
2.100 Summary
References

3 Superstrings
3.1 Supersymmetric Point Particles
3.2 Two-Dimensional Supersymmetry
3.3 Trees
3.4 Local Two-Dimensional Supersymmetry
3.5 Quantization
3.6 GSO Projection
3.7 Superstrings
3.8 Light Cone Quantization of the GS Action
3.9 Vertices and Trees
3.10 Summary
References

4 Conformal Field Theory and Kac——Moody Algebras
4.1 Conformal Field Theory
4.2 Superconformal Field Theory
4.3 Spin Fields
4.4 Superconformal Ghosts
4.5 Fermion Vertex
4.6 Spinors and Trees
4.7 Kac-Moody Algebras
4.8 Supersymmetry
4.9 Summary
References

5 Mulfiloops and Teichmuller Spaces
5.1 Unitarity
5.2 Single-Loop Amplitude
5.3 Harmonic Oscillators
5.4 Single-Loop Superstring Amplitudes
5.5 Closed Loops
5.6 Multiloop Amplitudes
5.7 Riemann Surfaces and Teichmiiller Spaces
5.8 Conformal Anomaly
5.9 Superstrings
5.10 Determinants and Singularities
5.11 Moduli Space and Grassmannians
5.12 Summary
References
Ⅱ Second Quantization and the Search for Geometry

6 Light Cone Field Theory
6.1 Why String Field Theory?
6.2 Deriving Point Particle Field Theory
6.3 Light Cone Field Theory
6.4 Interactions
6.5 Neumann Function Method
6.6 Equivalence of the Scattering Amplitudes
6.7 Four-String Interaction
6.8 Superstring Field Theory
6.9 Summary
References

7 BRST Field Theory
7.1 Covariant String Field Theory
7.2 BRST Field Theory
7.3 Gauge Fixing
7.4 Interactions
7.5 Wittens String Field Theory
7.6 Proof of Equivalence
7.7 Closed Strings and Superstrings
7.8 Summary
References
Ⅲ Phenomenology and Model Building

8 Anomalies and the Atiyah-Singer Theorem
8.1 Beyond GUT Phenomenology
8.2 Anomalies and Feynman Diagrams
8.3 Anomalies in the Functional Formalism
8.4 Anomalies and Characteristic Classes
8.5 Dirac Index
8.6 Gravitational and Gauge Anomalies
8.7 Anomaly Cancellation in Strings
8.8 Summary
References

9 Heterotic Strings and Compactification
9.1 Compactification
9.2 The Heterotic String
9.3 Spectrum
9.4 Covariant and Fermionic Formulations
9.5 Trees
9.6 Single-Loop Amplitude
9.7 Es and Kac——Moody Algebras
9.8 Lorentzian Lattices
9.9 Summary
References

10 Calabi——Yau Spaces and Orbifolds
10.1 Calabi-Yau Spaces
10.2 Review of de Rahm Cohomology
10.3 Cohomology and Homology
10.