Nonlinear realizations, the orbit method and Kohnʼs theorem

Andrzejewski, K.; Gonera, Joanna; Kosiński, Piotr

doi:10.1016/j.physletb.2012.04.042

Physics Letters B

2012

DOI: 10.1016/j.physletb.2012.04.042

|View full text |Cite

Nonlinear realizations, the orbit method and Kohnʼs theorem

K. Andrzejewski¹,

Joanna Gonera²,

Piotr Kosiński³

Abstract: The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart-Duval lift.

Help me understand this report

View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2013

2018

Publication Types

Select...

Article4

Relationship

Self Cite1

Independent3

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Renewed interest in Kohn's theorem on decomposing a system of charged particles in a magnetic field into center-of-mass and relative coordinates stems from relating it to the Newton-Hooke symmetry of the Landau problem [1][2][3][4][5].…”

mentioning

confidence: 99%

Newton–Hooke-type symmetry of anisotropic oscillators

Zhang¹,

Horváthy²,

Andrzejewski³

et al. 2013

Annals of Physics

Self Cite

View full text Add to dashboard Cite

The rotation-less Newton-Hooke -type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case.Star escape from a Galaxy is studied as application.

show abstract

mentioning

confidence: 99%

Newton–Hooke-type symmetry of anisotropic oscillators

Zhang¹,

Horváthy²,

Andrzejewski³

et al. 2013

Annals of Physics

Self Cite

View full text Add to dashboard Cite

show abstract

Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures

Bargueño

2015

Physics Letters A

View full text Add to dashboard Cite

Connections and dynamical trajectories in generalised Newton-Cartan gravity. II. An ambient perspective

Bekaert

Morand

2018

Journal of Mathematical Physics

109

View full text Add to dashboard Cite

Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are not unique, the arbitrariness being encoded in a tensor field whose type depends on the metric structure. Nonrelativistic structures typically fall under this scheme, the paradigmatic example being a contravariant degenerate metric whose kernel is spanned by a one-form. Torsionfree compatible (i.e. Galilean) connections are characterised by the gift of a two-form (the force field). Whenever the two-form is closed, the connection is said Newtonian. Such a nonrelativistic spacetime is known to admit an ambient description as the orbit space of a gravitational wave with parallel rays. The leaves of the null foliation are endowed with a nonrelativistic structure dual to the Newtonian one, dubbed Carrollian spacetime. We propose a generalisation of this unifying framework by introducing a new non-Lorentzian ambient metric structure of which we study the geometry. We characterise the space of (torsional) connections preserving such a metric structure which is shown to project to (resp. embed) the most general class of (torsional) Galilean (resp. Carrollian) connections.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Nonlinear realizations, the orbit method and Kohnʼs theorem

Cited by 4 publications

References 23 publications

Newton–Hooke-type symmetry of anisotropic oscillators

Newton–Hooke-type symmetry of anisotropic oscillators

Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures

Connections and dynamical trajectories in generalised Newton-Cartan gravity. II. An ambient perspective

Contact Info

Product

Resources

About