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Lectures on quantum field theory /
This book consists of the lectures for a two-semester course on quantum field theory, and as such is presented in a quite informal and personal manner. The course starts with relativistic one-particle systems, and develops the basics of quantum field theory with an analysis of the representations of...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2008.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Relativistic equations. 1.1. Introducion. 1.2. Notations. 1.3. Klein-Gordon equation. 1.4. Dirac equation. 1.5. References
- 2. Solutions of the Dirac equation. 2.1. Plane wave equation. 2.2. Normalization of the wave function. 2.3. Spin of the Dirac particle. 2.4. Continuity equation. 2.5. Dirac's hole theory. 2.6. Properties of the Dirac matrices. 2.7. References
- 3. Properties of the Dirac equation. 3.1. Lorentz transformations. 3.2. Covariance of the Dirac equation. 3.3. Transformation of bilinears. 3.4. Projection operators, completeness relation. 3.5. Helicity. 3.6. Massless Dirac particle. 3.7. Chirality. 3.8. Non-relativistic limit of the Dirac equation. 3.9. Electron in an external magnetic field. 3.10. Foldy-Wouthuysen transformation. 3.11. Zitterbewegung. 3.12. References
- 4. Representations of Lorentz and Poincaré groups. 4.1. Symmetry algebras. 4.2. Representations of the Lorentz group. 4.3. Unitary representations of the Poincaré group. 4.4. References
- 5. Free Klein-Gordon field theory. 5.1. Introduction. 5.2. Lagrangian density. 5.3. Quantization. 5.4. Field decomposition. 5.5. Creation and annihilation operators. 5.6. Energy eigenstates. 5.7. Physical meaning of energy eigenstates. 5.8. Green's functions. 5.9. Covariant commutation relations. 5.10. References
- 6. Self-interacting scalar field theory. 6.1. Nöther's theorem. 6.2. Self-interacting [symbol] theory. 6.3. Interaction picture and time evolution operator. 6.4. S-matrix. 6.5. Normal ordered product and Wick's theorem. 6.6. Time ordered products and Wick's theorem. 6.7. Spectral representation and dispersion relation. 6.8. References
- 7. Complex scalar field theory. 7.1. Quantization. 7.2. Field decomposition. 7.3. Charge operator. 7.4. Green's functions. 7.5. Spontaneous symmetry breaking and the Goldstone theorem. 7.6. Electromagnetic coupling. 7.7. References
- 8. Dirac field theory. 8.1. Pauli exclusion principle. 8.2. Quantization of the Dirac field. 8.3. Field decomposition. 8.4. Charge operator. 8.5. Green's functions. 8.6. Covariant anti-commutation relations. 8.7. Normal ordered and time ordered products. 8.8. Massless Dirac fields. 8.9. Yukawa interaction. 8.10. Feynman diagrams. 8.11. References
- 9. Maxwell field theory. 9.1. Maxwell's equations. 9.2. Canonical quantization. 9.3. Field decomposition. 9.4. Photon propagator. 9.5. Quantum electrodynamics. 9.6. Physical processes. 9.7. Ward-Takahashi identity in QED. 9.8. Covariant quantization of the Maxwell theory. 9.9. References
- 10. Dirac method for constrained systems. 10.1. Constrained systems. 10.2. Dirac method and Dirac bracket. 10.3. Particle moving on a sphere. 10.4. Relativistic particle. 10.5. Dirac field theory. 10.6. Maxwell field theory. 10.7. References
- 11. Discrete symmetries. 11.1. Parity. 11.2. Charge conjugation. 11.3. Time reversal. 11.4. CPT theorem. 11.5. References
- 12. Yang-Mills theory. 12.1. Non-Abelian gauge theories. 12.2. Canonical quantization of Yang-Mills theory. 12.3. Path integral quantization of gauge theories. 12.4. Path integral quantization of tensor fields. 12.5. References
- 13. BRST invariance and its consequences. 13.1. BRST symmetry. 13.2. Covariant quantization of Yang-Mills theory. 13.3. Unitarity. 13.4. Slavnov-Taylor identity. 13.5. Feynman rules. 13.6. Ghost free gauges. 13.7. References
- 14. Higgs phenomenon and the standard model. 14.1. Stückelberg formalism. 14.2. Higgs phenomenon. 14.3. The standard model. 14.4. References
- 15. Regularization of Feynman diagrams. 15.1. Introduction. 15.2. Loop expansion. 15.3. Cut-off regularization. 15.4. Pauli-Villars regularization. 15.5. Dimensional regularization. 15.6. References
- 16. Renormalization theory. 16.1. Superficial degree of divergence. 16.2. A brief history of renormalization. 16.3. Schwinger-Dyson equation. 16.4. BPHZ renormalization. 16.5. Renormalization of gauge theories. 16.6. Anomalous Ward identity. 16.7. References
- 17. Renormalization group and equation. 17.1. Gell-Mann-Low equation. 17.2. Renormalization group. 17.3. Renormalization group equation. 17.4. Solving the renormalization group equation. 17.5. Callan-Symanzik equation. 17.6. References.