de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch
 
Hilfe Wegweiser Impressum Kontakt Einloggen
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Forschungspapier

Group Fourier transform and the phase space path integral for finite dimensional Lie groups

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons26303

Raasakka,  Matti
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Externe Ressourcen
Es sind keine Externen Ressourcen verfügbar
Volltexte (frei zugänglich)

1111.6481
(Preprint), 131KB

Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

Raasakka, M. (in preparation). Group Fourier transform and the phase space path integral for finite dimensional Lie groups.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000E-EE8C-4
Zusammenfassung
We formulate a notion of group Fourier transform for a finite dimensional Lie group. The transform provides a unitary map from square integrable functions on the group to square integrable functions on a non-commutative dual space. We then derive the first order phase space path integral for quantum mechanics on the group by using a non-commutative dual space representation obtained through the transform. Possible advantages of the formalism include: (1) The transform provides an alternative to the spectral decomposition via representation theory of Lie groups and the use of special functions. (2) The non-commutative dual variables are physically more intuitive, since despite the non-commutativity they are analogous to the corresponding classical variables. The work is expected, among other possible applications, to allow for the metric representation of Lorentzian spin foam models in the context of quantum gravity.