Algebraic approach to the 1/N expansion in quantum field theory

Reviews in Mathematical Physics

Volumn 16, Issue 4, 2004, Pages 509-558

  Hollands, Stefan ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Algebraic methods; Large N expansion; Perturbation theory; Quantum field theory

Indexed keywords

EID: 13144283767     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X04002072     Document Type: Article

References (21)

1. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, Ann. Phys. (NY) 111 (1978) 61.
2. R. Brunetti, K. Fredenhagen and M. Köhler, The microlocal spectrum condition and Wick polynomials on curved spacetimes, Commun. Math. Phys. 180 (1996) 633-652.
3. R. Brunetti and K. Fredenhagen, "Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds, Commun. Math. Phys. 208 (2000) 623-661.
4. M. Dütsch and K. Fredenhagen, Algebraic quantum field theory, perturbation theory, and the loop expansion, Commun. Math. Phys. 219 (2001) 5, arXiv:hep-th/0001129; Perturbative algebraic field theory, and deformation quantization, to appear in Fields Inst. Commun. arXiv:hep-th/0101079.
5. M. Dütsch and K. Fredenhagen, Algebraic quantum field theory, perturbation theory, and the loop expansion, Commun. Math. Phys. 219 (2001) 5, arXiv:hep-th/0001129; Perturbative algebraic field theory, and deformation quantization, to appear in Fields Inst. Commun. arXiv:hep-th/0101079.
6. M. Dütsch and K. Fredenhagen, The master Ward identity and generalized Schwinger-Dyson equation in classical field theory, Commun. Math. Phys. 243 (2003) 275, arXiv:hep-th/0211242.
7. M. Dütsch and K. Fredenhagen: Causal Perturbation Theory in Terms of Retarded Products, and a Proof of the Action Ward Identity, hep-th/0403213.
8. M. Dütsch, T. Hurth and G. Scharf, Causal construction of Yang-Mills theories. 4. Unitarity, Nuovo Cim. A108 (1995) 737. See also references contained in this paper.
9. R. Haag, On quantum field theories, Dan. Mat. Fys. Medd. 29(12) (1955) 13; reprinted in Dispersion Relations and the Abstract Approach to Field Theory, ed. L. Klein (Gordon & Breach, NY, 1961).
10. R. Haag, On quantum field theories, Dan. Mat. Fys. Medd. 29(12) (1955) 13; reprinted in Dispersion Relations and the Abstract Approach to Field Theory, ed. L. Klein (Gordon & Breach, NY, 1961).
11. L. Hörmander, The Analysis of Linear Partial Differential Operators I, 2nd edn. (Springer-Verlag, 1990).
12. S. Hollands and R,. M. Wald, On the renormalization group in curved spacetime, Commun. Math. Phys. 237 (2003) 123-160, arXiv:gr-qc/0209029.
13. S. Hollands and R. M. Wald, Local Wick polynomials and time-ordered products of quantum fields in curved spacetime, Commun. Math. Phys. 223 (2001) 289, arXiv:gr-qc/0103074.
14. S. Hollands and R. M. Wald, Existence of local covariant time-ordered products of quantum fields in curved spacetime, Commun. Math. Phys. 231 (2002) 309, arXiv:gr-qc/0111108.
15. S. Hollands and R. M. Wald, Time ordered products of fields with derivatives, in preparation.
16. S. Hollands and W. Ruan, The state space of perturbative quantum field theory in curved space-times, Ann. Inst. H. Poincaré 3 (2002) 635, arXiv:gr-qc/0108032.
17. G. 't Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B72 (1974) 461.
18. T. Hurth and K. Skenderis, Quantum Noether method, Nucl. Phys. B541 (1999) 566, arXiv:hep-th/9803030.
19. G. Parisi, The theory of non-renormalizable interactions. The large N expansion, Nucl. Phys. B100 (1975) 368-388.
20. M. Reed and B. Simon, Methods of Modern Mathematical Physics I (Academic Press, New York, 1973).
21. G. Scharf, Finite Quantum Electrodynamics. The Causal Approach, 2nd edn. (Springer Verlag, 1995).