Fetching the paper…

Reading the bibliography…

Action-angle variables for dihedral systems on the circle · Around

2010

Action-angle variables for dihedral systems on the circle

Lechtenfeld, Olaf, Nersessian, Armen, Yeghikyan, Vahagn

Original
PDF
Post on X

Understand

A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N.

For such `dihedral systems' we construct the action-angle variables and establish a local equivalence with a free particle on the circle.
We perform the quantization of these systems in the action-angle variables and discuss the supersymmetric extension of this procedure.
By allowing radial motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2 three-particle rational Calogero models on R, which we also analyze.

Built on

E. Schrödinger, Proc. Roy. Irish Soc
1941
Earlier work this paper cites.
H. Goldstein, Classical Mechanics
1950
Earlier work this paper cites.
G.M. Fichtenholz, Foundations of Differential and Integral Calculus
1966
Earlier work this paper cites.
F. Calogero, J. Math. Phys. 10
1971
Earlier work this paper cites.
S. Flügge, Practical Quantum Mechanics 1
1971
Earlier work this paper cites.
V.I. Arnold, Mathematical methods in classical mechanics
1973
Earlier work this paper cites.
J. Wolfes, J. Math. Phys. 15
1977
Earlier work this paper cites.
P.W. Higgs, J. Phys. A 12
1979
Earlier work this paper cites.

Similar

E. Witten, Nucl. Phys. B 188
1981
Cited alongside, same era.
V.N. Shander, Darboux and Liuville theorem on supermanifolds
1983
Cited alongside, same era.
S. Woijechowski, Phys. Lett. A95
Original
1983
Cited alongside, same era.
A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series
1986
Cited alongside, same era.
A.O. Barut, A. Inomata, R. Wilson, J. Phys. A: Math. Gen. 20
1987
Cited alongside, same era.
O.M. Khudaverdian, A.P. Nersessian, Formulation of Hamiltonian mechanics with even and odd Poisson brackets
1987
Cited alongside, same era.

Then

S. Bellucci, A. Nersessian, Phys. Rev. D 73
2006
Later among the works it cites.
H. Kastrup, Fortschr. Physik 51
2007
Later among the works it cites.
A. Galajinsky, O. Lechtenfeld, K. Polovnikov, Phys. Lett. B 643
2007
Later among the works it cites.
S. Bellucci, S. Krivonos, A. Sutulin, Nucl. Phys. B 805
2008
Later among the works it cites.
T. Hakobyan, A. Nersessian, V. Yeghikyan, J. Phys. A 42
Original
2009
Later among the works it cites.
F. Tremblay, A.V. Turbiner, P. Winternitz, J. Phys. A 42
Original
2010
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

S.N.M. Ruijenaars, Comm. Math. Phys. 115

1988

Cited alongside, same era.

L. Feher, I. Tsutsui, T. Fulop, Nucl. Phys. B 715

2005

Cited alongside, same era.

C. Quesne, J. Phys. A 43

2010

Closest in time.

T. Hakobyan, S. Krivonos, O. Lechtenfeld, A. Nersessian, Phys. Lett. A 374

2010

Closest in time.