Geodesic
Breaking the space–time translation group in the dipole field model
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 163-176 
M. A. Soloviev. Breaking the space–time translation group in the dipole field model. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 163-176. http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a0/
@article{TMF_1998_115_2_a0,
     author = {M. A. Soloviev},
     title = {Breaking the space{\textendash}time translation group in the dipole field model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--176},
     year = {1998},
     volume = {115},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a0/}
}
TY  - JOUR
AU  - M. A. Soloviev
TI  - Breaking the space–time translation group in the dipole field model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 163
EP  - 176
VL  - 115
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a0/
LA  - ru
ID  - TMF_1998_115_2_a0
ER  - 
%0 Journal Article
%A M. A. Soloviev
%T Breaking the space–time translation group in the dipole field model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 163-176
%V 115
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a0/
%G ru
%F TMF_1998_115_2_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

The impossibility of constructing a translation-invariant physical space for the massless dipole field models in two and four dimensions follows from the Lebesgue integral theory. The method of proof may also be useful for studying space–time symmetries in other models with singular behavior in the infrared domain. To fix the Hilbert majorant structure associated with an indefinite metric, we impose the condition that the majorant structure inherit the homogeneity properties from the metric.

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

[2] G. Morchio, F. Strocchi, Ann. Inst. Henri Poincaré. A, 33 (1980), 251 | MR

[3] D. Zwanziger, Phys. Rev. D, 17 (1978), 457 | DOI | MR

[4] U. Moschella, F. Strocchi, Lett. Math. Phys., 19 (1990), 143 | DOI | MR | Zbl

[5] U. Moschella, J. Math. Phys., 31 (1990), 2480 | DOI | MR | Zbl

[6] G. Morchio, F. Strocchi, Nucl. Phys. B, 211 (1983), 471 | DOI | MR

[7] U. Moschella, F. Strocchi, Lett. Math. Phys., 24 (1992), 103 | DOI | MR | Zbl

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

[9] N. Danford, Dzh. Shvarts, Lineinye operatory, T. 1, IL, M., 1962

[10] M. A. Solovev, TMF, 105 (1995), 405 | Zbl

[11] M. A. Soloviev, Lett. Math. Phys., 41 (1997), 265 | DOI | MR | Zbl