Conformal invariance and rationality in an even dimensional quantum field theory

International Journal of Modern Physics A

Volumn 19, Issue 22, 2004, Pages 3605-3636

  Nikolov, N M ^a   Todorov, I T ^a,b,c  

^a INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY   (Bulgaria)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Conformal field theory; Elliptic functions; Gauge field Lagrangian; Modular forms; Operator product expansions; Rational correlation functions

Indexed keywords

CORRELATION ANALYSIS; DENSITY; MATHEMATICAL MODEL; MATHEMATICS; QUANTUM THEORY; REVIEW; SPACE; TEMPERATURE; TIME;

EID: 4944226054     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X04019342     Document Type: Review

References (26)

1. R. E. Borcherds, Proc. Nat. Acad. Sci. USA 83, 3068 (1986).
2. V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis of the n-dimensional Lorentz Group and its Application to Conformal Quantum Field Theory (Springer, Berlin, 1977).
3. V. K. Dobrev, V. B. Petkova, S. G. Petrova and I. T. Todorov, Phys. Rev. D13, 887 (1976).
4. J. S. Dowker, K. Kirsten, Nucl. Phys. B638, 405 (2002).
5. F. A. Dolan and H. Osborn, Nucl. Phys. B599, 459 (2001).
6. F. A. Dolan and H. Osborn, Nucl. Phys. B678, 491 (2004).
7. B. Eden, A. C. Petkou, C. Schubert and E. Sokatchev, Nucl. Phys. B607, 191 (2001).
8. E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves (AMS, 2001).
9. S. Ferrara, R. Gatto, A. Grillo and G. Parisi, Nuovo Cimento Lett. 4, 115 (1972).
10. E. S. Fradkin and M. Ya. Palchik, Phys. Rep. 300, 1 (1998); Conformal Quantum Field Theory in D-Dimensions (Kluwer, Dordrecht, 1996).
11. E. S. Fradkin and M. Ya. Palchik, Phys. Rep. 300, 1 (1998); Conformal Quantum Field Theory in D-Dimensions (Kluwer, Dordrecht, 1996).
12. R. Haag, Local Quantum Physics, Fields, Particles, Algebras (Springer, Berlin, 1992).
13. V. G. Kac, Vertex Algebras for Beginners, 2nd edn., AMS, ULS 10 (Providence, R.I., 1998).
14. G. Mack, Commun. Math. Phys. 55, 1 (1977).
15. N. M. Nikolov, Vertex algebras in higher dimensions and globally conformal invariant quantum field theory, to appear in Commun. Math. Phys., hep-th/0307235.
16. N. M. Nikolov, Ya. S. Stanev and I. T. Todorov, J. Phys. A: Math. Gen. 35, 2985 (2002).
17. N. M. Nikolov, Ya. S. Stanev and I. T. Todorov, Nucl. Phys. B670 [FS], 373 (2003).
18. N. M. Nikolov, Ya. S. Stanev and I. T. Todorov, Rational correlation functions of gauge invariant local fields in four dimensions, in Procs. of V Int. Workshop on Lie Theory and its Applications in Physics (Varna, June 2003), eds. H.-D. Doebner and V. K. Dobrev (World Scientific, Singapore, 2004).
19. N. M. Nikolov and I. T. Todorov, Commun. Math. Phys. 218, 417 (2001).
20. N. M. Nikolov and I. T. Todorov, Finite temperature correlation functions and modular forms in a globally conformal invariant QFT, ICTP preprint: IC/2003/165; hep-th/0403191.
21. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (W. A. Benjamin, 1964; Princeton University Press, Princeton, New Jersey, 2000).
22. I. T. Todorov, Local field representations of the conformal group and their applications, in Mathematics and Physics. Lectures on Recent Results, Vol. 1, ed. L. Streit (World Scientific, Singapore, 1985), pp. 195-338.
23. I. T. Todorov, Infinite dimensional Lie algebras in conformal QFT models, in Conformal Groups and Related Symmetries. Physical Results and Mathematical Background, Lecture Notes in Physics 261, eds. A. O. Barut and H.-D. Doebner (Springer, Berlin, 1986), pp. 387-443.
24. I. T. Todorov, M. C. Mintchev and V. B. Petkova, Conformal Invariance in Quantum Field Theory (Scuola Normale Superiore, Pisa, 1978).
25. D. Zagier, Introduction to modular forms, in From Number Theory to Physics, 2nd edn., eds. M. Waldschmidt (Springer, 1995), pp. 238-291.
26. Y. Zhu, J. Amer. Math. Soc. 9 (1), 237 (1996).