Geodesic
Light-cone Yang--Mills mechanics: $SU(2)$ vs.~$SU(3)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 62-73

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

We investigate the light-cone $SU(n)$ Yang–Mills mechanics formulated as the leading order of the long-wavelength approximation to the light-front $SU(n)$ Yang–Mills theory. In the framework of the Dirac formalism for degenerate Hamiltonian systems, for models with the structure groups $SU(2)$ and $SU(3)$, we determine the complete set of constraints and classify them. We show that the light-cone mechanics has an extended invariance{:} in addition to the local $SU(n)$ gauge rotations, there is a new local two-parameter Abelian transformation, not related to the isotopic group, that leaves the Lagrangian system unchanged. This extended invariance has one profound consequence. It turns out that the light-cone $SU(2)$ Yang–Mills mechanics, in contrast to the well-known instant-time $SU(2)$ Yang–Mills mechanics, represents a classically integrable system. For calculations, we use the technique of Gröbner bases in the theory of polynomial ideals.
Keywords: gauge symmetry, Hamiltonian system, Gröbner basis. 
@article{TMF_2008_155_1_a5,
     author = {V. P. Gerdt and Yu. G. Palii and A. M. Khvedelidze},
     title = {Light-cone {Yang--Mills} mechanics: $SU(2)$ vs.~$SU(3)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {62--73},
     publisher = {mathdoc},
     volume = {155},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a5/}
}
TY  - JOUR
AU  - V. P. Gerdt
AU  - Yu. G. Palii
AU  - A. M. Khvedelidze
TI  - Light-cone Yang--Mills mechanics: $SU(2)$ vs.~$SU(3)$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 62
EP  - 73
VL  - 155
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a5/
LA  - ru
ID  - TMF_2008_155_1_a5
ER  - 
%0 Journal Article
%A V. P. Gerdt
%A Yu. G. Palii
%A A. M. Khvedelidze
%T Light-cone Yang--Mills mechanics: $SU(2)$ vs.~$SU(3)$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 62-73
%V 155
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a5/
%G ru
%F TMF_2008_155_1_a5
V. P. Gerdt; Yu. G. Palii; A. M. Khvedelidze. Light-cone Yang--Mills mechanics: $SU(2)$ vs.~$SU(3)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 62-73. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a5/