Scattering theory for quantum fields with indefinite metric

Communications in Mathematical Physics

Volumn 216, Issue 3, 2001, Pages 491-513

  Albeverio, Sergio ^a   Gottschalk, Hanno ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035529587     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000332     Document Type: Article

References (35)

1. 1. Albeverio, S., Gottschalk, H., Wu, J.-L.: Convoluted generalized white noise, Schwinger functions and their continuation to Wightman functions. Rev. Math. Phys. 8, No. 6, 763 (1996)
2. 2. Albeverio, S., Gottschalk, H., Wu, J.-L.: Models of local relativistic quantum fields with indefinite metric (in all dimensions). Commun. Math. Phys. 184, 509 (1997)
3. 3. Albeverio, S., Gottschalk, H., Wu, J.-L.: Nontrivial scattering amplitudes for some local relativistic quantum field models with indefinite metric. Phys. Lett. B 405, 243 (1997)
4. 4. Albeverio, S., Gottschalk, H., Wu, J.-L.: Scattering behaviour of quantum vector fields obtained from Euclidean covariant SPDEs. Rep. on Math. Phys. 44, 1/2, 21-28 (1999)
5. 5. Albeverio, S., Iwata, K., Kolsrud, T.: Random fields as solutions of the inhomogenous quaternionic Cauchy-Riemann equation. I. Invariance and analytic continuation . Commun. Math. Phys. 132, 550 (1990)
6. 6. Araki, H.: On a pathology in indefinite inner product spaces. Commun. Math. Phys. 85, 121 (1982)
7. 7. Baumgärtel, H., Wollenberg, M.: A class of nontrivial weakly local massive Wightman fields with interpolating properties. Commun. Math. Phys. 94, 331 (1984)
8. 8. Becker, C., Gielerak, R., Ługiewicz, P.: Covariant SPDEs and quantum Held structures. J. Phys. A 31, 231-258 (1998)
9. 9. Bleuler, K.: Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen. Helv. Phys. Acta 23, 567 (1950)
10. 10. Bogulubov, N.N., Logunov, A.A., Ossak, A.I., Todorov, I.T.: General principles of quantum field theories. Amsterdam: Kluwer Academic Publishers, 1990
11. 11. Borchers, H.-J.: Algebraic aspects of Wightman field theory. In: Statistical Mechanics and Field Theory, Ed. R.N. Sen and C. Weil, Jerusalem/London: Halsted Press, New York/Israel Universities Press, 1972. pp. 31-80
12. 12. Contantinescu, E: Distributionen und ihre Anwendung in der Physik. Stuttgart: Teubner, 1973
13. 13. Doplicher, S.: An algebraic spectrum condition. Commun. Math. Phys. 1, 1 (1965)
14. 14. Epstein, H.: Some analytic properties of scattering amplitudes in quantum field theory. In: Axiomatic quantum field theory, Proc. 1965 Brandeis University Summer Scool on Theoret. Phys., Ed. M. Chretien, S. Deser, New York: Gordon and Breach, 1966
15. 15. Fadeev, L.D., Popov, V.N.: Feynman diagrams for the Yang-Mills field. Phys. Lett. B 25, 29 (1967)
16. 16. Gottschalk, H.: Green's functions for scattering in local relativistic QFT. Dissertation, Bochum 1998
17. 17. Gottschalk, H.: A characterization of locality in momentum space. Lett. Math. Phys.50, 259-273 (1999)
18. 18. Gupta, S.N.: Theory of longitudinal photons in quantum electrodynamics. Proc. Phys. Soc. A 63, 681 (1950)
19. 19. Haag, R.: Quantum field theories with composite particles and aymptotic condition. Phys. Rev. 112, 669 (1958)
20. 20. Hepp, K.: On the connection between the LSZ and Wightman quantum field theory. Commun. Math. Phys. 1, 95 (1965)
21. 21. Hoffmann, G.: The Hilbert space structure condition for quantum field theories with indefinite metric and transformations with linear functionals. Lett. Math. Phys. 42, 281 (1997)
22. 22. Hoffmann, G.: On GNS representations on inner product spaces: I. The structure of the representation space. Commun. Math. Phys. 191, 299 (1998)
23. 23. Lehmann, H., Symanzik, K., Zimmermann, W.: Zur Formulierung quantisierter Feldtheorien. Il Nuovo Cimento 1, 205 (1954)
24. 24. Johnson, G.E.: Interacting quantum fields. Rev. Math. Phys. 11 7, 881-928 (1999) with Erratum: A Comment on Interacting quantum fields. Rev. Math. Phys. 12, 687-689 (2000)
25. 25. Mintchev, M.: Quantization in indefinite metric. J. Phys. A 13, 1841-1859 (1980)
26. 26. Morchio, G., Strocchi, F.: Infrared singularities, vacuum structure and pure phases in local quantum field theory. Ann. Inst. H. Poincare', 33, 251 (1980)
27. 27. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. II + III, San Diego: Academic Press, 1979
28. 28. Ruelle, D.: On the asymptotic condition in quantum field theory. Helv. Phys. Acta 35, 147 (1962)
29. 29. Scheibe, E.: Über Feldtheorien inZustandsräumen mit indefiniter Metrik. Max-Planck-Institut für Physik und Astrophysik, München, 1960
30. 30. Schneider, W.: S-Matrix und interpolierende Felder. Helv. Phys. Acta 39, 81 (1966)
31. 31. Streater, R.F., Wightman, A.S.: PCT, spin and statistics, and all that. New York, Amsterdam: Benjamin, 1964
32. 32. Strocchi, F.: Selected topics on the general properties of quantum field theory. Lecture Notes in Physics 51, Singapore-New York-London-Hong Kong: World Scientific, 1993
33. 33. Weinberg, S.: The quantum theory of fields. Vol. I, Cambridge: Cambridge Univ. Press, 1995
34. 34. Yang, C.N., Feldman, D.: The S-matrix in the Heisenberg representation. Phys. Rev. 79, 972 (1950)
35. 35. Yngvason, J.: On the algebra of test functions for field operators. Commun. Math. Phys. 34, 315 (1973)