Geodesic
On a generalization of the gauge principle at high energies
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 2, pp. 197-206 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A model of a Euclidean gauge theory that describes a system of interacting scalar and vector fields and is based on a more general concept of the field itself in the region of high energies is constructed. A key part is played by the Lobachevskii momentum 4-space with radius of curvature $M$, this parameter $M$ being interpreted as a new physical constant (“fundamental mass”). Expansion with respect to unitary representations of the group of motions of the Lobachevskii $p$ space plays the part of Fourier transformation. After transition to the corresponding new configuration representation, the basic equations of the theory become differential–difference equations with a step of order $M$. In this representation local gauge transformations of the matter and vector fields are defined. Because the theory contains the “fundamental mass” $M$, the law of the gauge transformation of the vector field is modified significantly and appears as a combination of standard Yang–Mills transformations and gauge transformations characteristic of the theory of a vector field on a lattice. However, this last does not break the Euclidean $0(4)$ invariance of the model. In the low-energy approximation ($M\to\infty$) the theory is equivalent to the standard theory. 
@article{TMF_1990_83_2_a3,
     author = {V. G. Kadyshevskii and D. V. Fursaev},
     title = {On~a~generalization of~the gauge principle at~high energies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--206},
     year = {1990},
     volume = {83},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a3/}
}
TY  - JOUR
AU  - V. G. Kadyshevskii
AU  - D. V. Fursaev
TI  - On a generalization of the gauge principle at high energies
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1990
SP  - 197
EP  - 206
VL  - 83
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a3/
LA  - ru
ID  - TMF_1990_83_2_a3
ER  - 
%0 Journal Article
%A V. G. Kadyshevskii
%A D. V. Fursaev
%T On a generalization of the gauge principle at high energies
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1990
%P 197-206
%V 83
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a3/
%G ru
%F TMF_1990_83_2_a3
V. G. Kadyshevskii; D. V. Fursaev. On a generalization of the gauge principle at high energies. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 2, pp. 197-206. http://geodesic.mathdoc.fr/item/TMF_1990_83_2_a3/

[1] Kadyshevsky V. G., Nucl. Phys., B141 (1978), 477–496 ; Proc. of Intern. Integrat. Conf. on Group Theory and Math. Physics (Austin, Texas, 1978) ; Кадышевский В. Г., ЭЧАЯ, 11:1 (1980), 5–39 | DOI | MR | MR

[2] Kadyshevsky V. G., Mateev M. D., Phys. Lett., 106B (1981), 139–142 | DOI

[3] Kadyshevsky V. G., Mateev M. D., Nuovo Cim., 87A:3 (1985), 324–349 | DOI

[4] Donkov A. D. i dr., Trudy VII Mezhd. sov. po problemam kvantovoi teorii polya (Alushta, 1984); Препринт Д2-84-366, ОИЯИ, Дубна, 1984, С. 172.; Chizhov M. V. et al., Nuovo Cim., 87A:3 (1985), 350–372 ; 4, 373–396 | DOI | MR

[5] Donkov A. D. i dr., Izv. AN SSSR. Ser. fiz., 46:9 (1982), 1772–1775; Ибадов Р. М., Чижов М. В., Изв. АН УзССР. Сер. физ.-мат. наук, 1983, No 5, 38–40

[6] Ibadov R. M., Izv. AN UzSSR. Ser. fiz.-mat. nauk, 1984, no. 3, 44–46

[7] Kadyshevskii V. G., “Kvantovaya teoriya polya i «maksimon» Markova”, Doklad na III Mezhd. seminare «Kvantovaya teoriya gravitatsii» (Moskva, 1984) ; Препринт Р2-84-753, ОИЯИ, Дубна, 1984 | MR | Zbl

[8] Ibadov R. M., Kadyshevskii V. G., K teorii polya s fundamentalnoi massoi, Preprint R2-86-830, OIYaI, Dubna, 1986

[9] Ibadov R. M., Kadyshevskii V. G., O preobrazovaniyakh supersimmetrii v teorii polya s fundamentalnoi massoi, Preprint R2-86-835, OIYaI, Dubna, 1986

[10] Kadyshevskii V. G., Fursaev D. V., DAN SSSR, 306:4 (1989), 856–858 | MR

[11] Kadyshevsky V. G., Mateev M. D., Mir-Kasimov B. M., On solution of the Charge Quantization Problem, Preprint E2-88-92, JINR, Dubna, 1975 | MR

[12] Shapiro I. S., DAN SSSR, 106 (1956), 647–650; ЖЭТФ, 43 (1962), 1727–1730

[13] Kadyshevsky V. G., Mir-Kasimov R. M., Skachkov N. B., Nuovo Cim., 55A (1968), 233–257 | DOI

[14] Kadyshevskii V. G., Mir-Kasimov R. M., Skachkov N. B., EChAYa, 2:3 (1972), 635–690

[15] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Fizmatgiz, M., 1965 | MR

[16] Perelomov A. M., Obobschennye kogerentnye sostoyaniya i ikh primeneniya, Nauka, M., 1987 | MR

[17] Sherman T. O., Transactions of the American Mathematical Society, 209 (1975), 1–31 | DOI | MR | Zbl