Noncommutative deformations of Wightman quantum field theories

Journal of High Energy Physics

Volumn 2008, Issue 9, 2008, Pages

  Grosse, Harald ^a   Lechner, Gandalf ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Field theories in higher dimensions; Non commutative geometry; Nonperturbative effects

Indexed keywords

EID: 58149308639     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/09/131     Document Type: Article

References (34)

1. S. Doplicher, K. Fredenhagen and J.E. Roberts, The quantum structure of space-time at the Planck scale and quantum fields 1995 Comm. Math. Phys. 172 187 [hep-th/0303037]
2. R.J. Szabo, Quantum field theory on noncommutative spaces 2003 Phys. Rep. 378 207 [hep-th/0109162]
3. 4 in the matrix base 2005 Comm. Math. Phys. 256 305 [hep-th/0401128]
4. D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Field theory on noncommutative spacetimes: quasiplanar Wick products 2005 Phys. Rev. D 71 025022 [hep-th/0408204]
5. V. Rivasseau, Non-commutative renormalization 2007 Séminaire Poincaré X 15 [0705.0705]
6. H. Grosse and G. Lechner, Wedge-local quantum fields and noncommutative Minkowski space 2007 J. High Energy Phys. JHEP11(2007)012 [0706.3992]
7. E. Akofor, A.P. Balachandran and A. Joseph, Quantum fields on the Groenewold-Moyal Plane 2008 Int. J. Mod. Phys. A 23 1637
8. H. Grosse and F. Vignes-Tourneret, Minimalist translation-invariant non-commutative scalar field theory [0803.1035]
9. R. Gurau, J. Magnen, V. Rivasseau and A. Tanasa, A translation-invariant renormalizable non-commutative scalar model [0802.0791]
10. 4 theory 2004 Eur. Phys. J. C 35 277 [hep-th/0402093]
11. 4 theory 2007 Eur. Phys. J. C 50 661 [hep-th/0610224]
12. 4 theory to all orders 2007 Phys. Lett. B 649 95 [hep-th/0612251]
13. L. lvarez-Gaumé and M.A. Vazquez-Mozo, General properties of noncommutative field theories 2003 Nucl. Phys. B 668 293 [hep-th/0305093]
14. M. Chaichian, M.N. Mnatsakanova, K. Nishijima, A. Tureanu and Y.S. Vernov, Towards an axiomatic formulation of noncommutative quantum field theory [hep-th/0402212]
15. M.A. Soloviev, On the failure of microcausality in noncommutative field theories 2008 Phys. Rev. D 77 125013 [0802.0997]
16. H.-J. Borchers, D. Buchholz and B. Schroer, Polarization-free generators and the S-matrix 2001 Comm. Math. Phys. 219 125 [hep-th/0003243]
17. D. Buchholz and S.J. Summers, Warped convolutions: a novel tool in the construction of quantum field theories [0806.0349]
18. R. Haag, Local quantum physics: fields, particles, algebras (Springer-Verlag, Berlin) Germany (1996)
19. N.N. Bogolubov, A.A. Logunov and I.T. Todorov, Introduction to axiomatic quantum field theory W.A. Benjamin Inc., U.S.A. (1975)
20. R.F. Streater and A. Wightman, PCT, spin and statistics, and all that Benjamin-Cummings, Reading U.S.A. (1964)
21. R. Jost, The general theory of quantized fields American Mathematical Society, Providence U.S.A. (1965)
22. H.J. Borchers, On structure of the algebra of field operators 1962 Nuovo Cim. 24 214
23. G. Lassner and A. Uhlmann, On positive functionals on algebras of test functions for quantum fields 1968 Commun. Math. Phys. 7 152
24. K. Schmüdgen, Unbounded operator algebras and representation theory Birkhäuser, Berlin Germany (1990)
25. A.P. Balachandran, A. Pinzul, B.A. Qureshi and S. Vaidya, S-matrix on the Moyal plane: locality versus Lorentz Invariance 2008 Phys. Rev. D 77 025020 [0708.1379]
26. M. Chaichian, K. Nishijima and A. Tureanu, Spin-statistics and CPT theorems in noncommutative field theory 2003 Phys. Lett. B 568 146 [hep-th/0209008]
27. E. Akofor, A.P. Balachandran, S.G. Jo and A. Joseph, Quantum Fields on the Groenewold-Moyal Plane: c, P, T and CPT 2007 J. High Energy Phys. JHEP08(2007)045 [0706.1259]
28. L.J. Thomas and E.H. Wichmann, On the causal structure of Minkowski space-time 1997 J. Math. Phys. 38 5044
29. C.-S. Chu, K. Furuta and T. Inami, Locality, causality and noncommutative geometry 2006 Int. J. Mod. Phys. A 21 67 [hep-th/0502012]
30. B. Schroer, Modular localization and the bootstrap-formfactor program 1997 Nucl. Phys. B 499 547 [hep-th/9702145]
31. G. Lechner, Polarization-free quantum fields and interaction 2003 Lett. Math. Phys. 64 137 [hep-th/0303062]
32. D. Buchholz and G. Lechner, Modular nuclearity and localization 2004 Annales Henri Poincaré 5 1065 [math-ph/0402072]
33. D. Buchholz and S.J. Summers, String-localized fields in a strongly nonlocal model 2007 J. Phys. A: Math. Gen. 40 2147 [math-ph/0512060]
34. G. Lechner, Construction of quantum field theories with factorizing S-matrices 2008 Comm. Math. Phys. 277 821 [math-ph/0601022]