Non-perturbative methods in 2 dimensional quantum field theory /
The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques...
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| Main Author: | |
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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Edition: | 2nd ed. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- 1. Introduction
- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions
- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion
- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion
- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation
- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks
- 7. Non-linear [symbol] models
- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion
- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion
- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion
- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion
- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions
- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion
- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion
- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion
- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion
- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion
- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions
- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion
- 19. Final remarks.
