Construction of quantum field theories with factorizing S-matrices

Communications in Mathematical Physics

Volumn 277, Issue 3, 2008, Pages 821-860

  Lechner, Gandalf ^a  

^a Erwin Schrodinger International Institute for Mathematical Physics   (Austria)

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[No Author keywords available]

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EID: 37249074978     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0381-5     Document Type: Article

References (63)

1. Abdalla E., Abdalla M.C.B. and Rothe D. (1991). Non-perturbative Methods in Two-Dimensional Quantum Field Theory. World Scientific Publishing, Singapore
2. Araki, H.: Mathematical Theory of Quantum Fields. Int. Series of Monographs on Physics 101, Oxford: Oxford University Press, 1999
3. Arinshtein A.E., Fateev V.A. and Zamolodchikov A.B. (1979). Quantum S-matrix of the (1 + 1)-dimensional Toda chain. Phys. Lett. B 87: 389-392
4. Babujian H. and Karowski M. (2002). Exact form factors in integrable quantum field theories: the sine-Gordon model (II). Nucl. Phys. B 620: 407-455
5. Babujian H. and Karowski M. (2003). Exact form factors for the scaling ZN-Ising and the affine AN-1-Toda quantum field theories. Phys. Lett. B 575: 144-150
6. Babujian H. and Karowski M. (2004). Towards the construction of Wightman functions of integrable quantum field theories. Int. J. Mod. Phys. A 19S2: 34-49
7. Balog, J., Weisz, P.: Construction and clustering properties of the 2-d non-linear sigma-model form factors: O(3), O(4), large n examples. http://arxiv.org/list/hepth/0701202, 2007
8. Bisognano J.J. and Wichmann E.H. (1975). On the Duality Condition for a Hermitian Scalar Field. J. Math. Phys. 16: 985-1007
9. Bisognano J.J. and Wichmann E.H. (1976). On the Duality Condition for Quantum Fields. J. Math. Phys. 17: 303-321
10. Bochner S. and Martin W.T. (1948). Several Complex Variables. Princeton University Press, Princeton, NJ
11. Borchers H.-J. (1992). The CPT theorem in two-dimensional theories of local observables. Commun. Math. Phys. 143: 315-332
12. Borchers H.-J. (1998). Half-sided Translations and the Type of von Neumann Algebras. Lett. Math. Phys. 44: 283-290
13. Borchers H.-J. (2000). On revolutionizing quantum field theory with Tomita's modular theory. J. Math. Phys. 41: 3604-3673
14. Borchers H.-J., Buchholz D. and Schroer B. (2001). Polarization-free generators and the S-matrix. Commun. Math. Phys. 219: 125-140
15. Buchholz D., D'Antoni C. and Longo R. (1990). Nuclear Maps and Modular Structures. 1. General Properties. J. Funct. Anal. 88: 233-250
16. Buchholz D., D'Antoni C. and Longo R. (1990). Nuclear Maps and Modular Structures. 2. Applications to Quantum Field Theory. Commun. Math. Phys. 129: 115-138
17. Buchholz D. and Lechner G. (2004). Modular nuclearity and localization. Ann. H. Poincaré 5: 1065-1080
18. Buchholz D. and Summers S.J. (2004). Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties. J. Math. Phys. 45: 4810-4831
19. Buchholz, D., Summers, S.J.: Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools. http://arxiv.org/list/math-ph/0509047, 2005
20. Buchholz, D., Summers, S.J.: String- and Brane-Localized Causal Fields in a Strongly Nonlocal Model. http://arxiv.org/list/math-ph/0512060v2, 2005
21. Buchholz D. and Wichmann E.H. (1986). Causal Independence and the Energy Level Density of States in Local Quantum Field Theory. Commun. Math. Phys. 106: 321-344
22. Connes A. (1973). Une classification des facteurs de type III. Ann. Scient. Éc. Norm. Sup. 6: 133-252
23. D'Antoni C. and Longo R. (1983). Interpolation by type I factors and the flip automorphism. J. Funct. Anal. 51: 361-371
24. Doplicher S. and Longo R. (1984). Standard and split inclusions of von Neumann algebras. Invent. Math. 75: 493-536
25. Dorey, P.: Exact S-matrices. http://arxiv.org/list/hepth/9810026, 1998
26. Driessler W. (1975). Comments on Lightlike Translations and Applications in Relativistic Quantum Field Theory. Commun. Math. Phys. 44: 133-141
27. Eden R.J., Landshoff P.V., Olive D.I. and Polkinghorne J.C. (1966). The Analytic S-matrix. Cambridge University Press, Cambridge
28. Epstein H. (1960). Generalization of the Edge-of-the-Wedge Theorem. J. Math. Phys. 1: 524-531
29. Epstein, H.: Some Analytic Properties of Scattering Amplitudes in Quantum Field Theory. In: Brandeis University Summer Institute in Theoretical Physics 1965, Axiomatic Field Theory Vol. 1, M. Chretien, S. Deser, eds., New York: Gordon and Breach, 1966
30. Fring A., Mussardo G. and Simonetti P. (1993). Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model. Nucl. Phys. B 393: 413-441
31. Fröhlich J. (1975). Quantized Sine Gordon Equation with a Non-Vanishing Mass Term in Two Space-Time Dimensions. Phys. Rev. Lett. 34: 833-836
32. Fröhlich, J.: Quantum Sine Gordon Equation and Quantum Solitons in Two Space-Time Dimensions. In: Renormalization Theory, G. Velo, A.S. Wightman, eds., Series C - Math. and Phys. Sciences, Vol 23, Dordrecht-Boston: Reidel, 1976, pp. 371-414
33. Glimm J. and Jaffe A. (1981). Quantum Physics - A Functional Integral Point of View. Springer, New York
34. Haag R. (1992). Local Quantum Physics, 2nd edition. Springer, New York
35. Hepp, K.: On the connection between Wightman and LSZ quantum field theory. In: Brandeis University Summer Institute in Theoretical Physics 1965, Axiomatic Field Theory Vol. 1, M. Chretien, S. Deser, eds., New York: Gordon and Breach, 1966, pp. 135-246
36. Iagolnitzer D. (1978). Factorization of the multiparticle S-matrix in two-dimensional space-time models. Phys. Rev. D 18: 1275-1285
37. Iagolnitzer D. (1993). Scattering in Quantum Field Theories. Princeton University Press, Princeton, NJ
38. Jarchow H. (1981). Locally convex spaces. Teubner, Stuttgart
39. Kadison R.V. and Ringrose J.R. (1986). Fundamentals of the Theory of Operator Algebras. Vol. II: Advanced Theory. Academic Press, London-New York
40. Karowski M., Thun H.J., Truong T.T. and Weisz P.H. (1977). On the uniqueness of a purely elastic S-matrix in (1+1) dimensions. Phys. Lett. 67 B: 321-322
41. Kosaki H. (1984). On the continuity of the map φ |φ| from the predual of a W*-algebra. J. Funct. Anal. 59: 123-131
42. Lechner G. (2003). Polarization-Free Quantum Fields and Interaction. Lett. Math. Phys. 64: 137-154
43. Lechner G. (2005). On the existence of local observables in theories with a factorizing S-matrix. J. Phys. A 38: 3045-3056
44. Lechner, G.: Towards the construction of quantum field theories from a factorizing S-matrix. In: Rigorous Quantum Field Theory, Boutet de Monvel, A., Buchholz, D., Iagolnitzer, D., Moschella, U., eds., Progress in Mathematics Vol. 251, Basel-Boston: Birkhäuser, 2006
45. Lechner, G.: On the Construction of Quantum Field Theories with Factorizing S-Matrices. PhD thesis (advisor: D. Buchholz), Göttingen University, 2006
46. Liguori A. and Mintchev M. (1995). Fock representations of quantum fields with generalized statistics. Commun. Math. Phys. 169: 635-652
47. Longo R. (1979). Notes on algebraic invariants for noncommutative dynamical systems. Commun. Math. Phys. 69: 195-207
48. Longo R. and Rehren K.-H. (2004). Local fields in boundary conformal QFT. Rev. Math. Phys. 16: 909-960
49. Müger M. (1998). Superselection Structure of Massive Quantum Field Theory in 1+1 Dimensions. Rev. Math. Phys. 10: 1147-1170
50. Mund J., Schroer B. and Yngvason J. (2006). String-Localized Quantum Fields and Modular Localization. Commun. Math. Phys. 268: 621-672
51. Pietsch A. (1972). Nuclear Locally Convex Spaces. Springer, New York
52. Reed M. and Simon B. (1975). Methods of Modern Mathematical Physics, Vol II: Fourier Analysis, Self-Adjointness. Academic Press, New York
53. Reed M. and Simon B. (1979). Methods of Modern Mathematical Physics, Vol III: Scattering Theory. Academic Press, New York
54. Sakai S. (1971). C*-Algebras and W*-Algebras. Springer, New York
55. Schroer B. (1997). Modular localization and the bootstrap-formfactor program. Nucl. Phys. B 499: 547-568
56. Schroer B. (1999). Modular wedge localization and the d = 1+1 formfactor program. Ann. Phys. 275: 190-223
57. Schroer B. (2005). Constructive proposals for QFT based on the crossing property and on lightfront holography. Ann. Phys. 319: 48-91
58. Schroer B. and Wiesbrock H.-W. (2000). Modular constructions of quantum field theories with interactions. Rev. Math. Phys. 12: 301-326
59. Smirnov F.A. (1992). Form Factors in Completely Integrable Models of Quantum Field Theory. World Scientific, Singapore
60. Stein E. and Weiss G. (1971). Introduction to Fourier Analysis on Euclidian Spaces. Princeton University Press, Princeton, NJ
61. Streater R.F. and Wightman A.S. (1980). PCT, Spin and Statistics and All That, 3rd edition. Princeton University Press, Princeton, NJ
62. Takesaki M. (1979). Theory of Operator Algebras I. Springer, New York
63. Zamolodchikov A.B. and Zamolodchikov A.B. (1979). Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field models. Ann. Phys. 120: 253-291