Geodesic
Axiomatic formulations of nonlocal and noncommutative field theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 257-269 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin–statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley–Wiener–Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced with that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin–statistics theorems in this enlarged framework.
Keywords: nonlocal quantum fields, causality, noncommutative field theory, Wightman functions, analytic functionals, Paley–Wiener–Schwartz theorem. 
@article{TMF_2006_147_2_a3,
     author = {M. A. Soloviev},
     title = {Axiomatic formulations of nonlocal and noncommutative field theories},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {257--269},
     year = {2006},
     volume = {147},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/}
}
TY  - JOUR
AU  - M. A. Soloviev
TI  - Axiomatic formulations of nonlocal and noncommutative field theories
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 257
EP  - 269
VL  - 147
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/
LA  - ru
ID  - TMF_2006_147_2_a3
ER  - 
%0 Journal Article
%A M. A. Soloviev
%T Axiomatic formulations of nonlocal and noncommutative field theories
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 257-269
%V 147
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/
%G ru
%F TMF_2006_147_2_a3
M. A. Soloviev. Axiomatic formulations of nonlocal and noncommutative field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 257-269. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/

[1] R. Jost, The General Theory of Quantized Fields, AMS, Providence, RI, 1965 | MR | Zbl

[2] R. Striter, A. Vaitman, RST, spin i statistika i vse takoe, Nauka, M., 1966

[3] N. N. Bogolyubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, Obschie printsipy kvantovoi teorii polya, Nauka, M., 1987 | MR

[4] O. Steinmann, Commun. Math. Phys., 18 (1970), 179 | DOI | MR | Zbl

[5] M. A. Solovev, TMF, 121 (1999), 139 | DOI | MR | Zbl

[6] M. A. Solovev, TMF, 143 (2005), 195 | DOI | MR

[7] B. Schroer, Ann. Phys., 319 (2005), 92 | DOI | MR | Zbl

[8] N. Seiberg, E. Witten, JHEP, 9909 (1999), 032 | DOI | MR

[9] L. Álvarez-Gaumé, M. A. Vázquez-Mozo, Nucl. Phys. B, 668 (2003), 293 | DOI | MR | Zbl

[10] C.-S. Chu, K. Furuta, T. Inami, Int. J. Mod. Phys. A, 21 (2006), 67 ; hep-th/0502012 | DOI | MR | Zbl

[11] V. E. Hubeny, M. Rangamani, S. F. Ross, JHEP, 0507 (2005), 037 | DOI | MR

[12] D. H. T. Franco, C. M. M. Polito, J. Math. Phys., 46 (2005), 083503 | DOI | MR | Zbl

[13] M. A. Soloviev, J. Math. Phys., 39 (1998), 2635 | DOI | MR | Zbl

[14] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, t. 2, Fizmatlit, M., 1958 | MR | Zbl

[15] A. G. Smirnov, J. Math. Phys., 44 (2003), 2058 | DOI | MR | Zbl

[16] M. A. Soloviev, J. Math. Phys., 45 (2004), 1944 | DOI | MR | Zbl

[17] M. A. Soloviev, Carrier cones of analytic functionals, hep-th/0507011

[18] L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, t. 1, Mir, M., 1986 | MR

[19] M. A. Solovev, TMF, 128 (2001), 492 | DOI | MR | Zbl

[20] M. Chaichian, P. P. Kulish, K. Nishijima, A. Tureanu, Phys. Lett. B, 604 (2004), 98 | DOI | MR | Zbl