English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We formulate a notion of group Fourier transform for a finite dimensional Liegroup. The transform provides a unitary map from square integrable functions onthe group to square integrable functions on a non-commutative dual space. Wethen derive the first order phase space path integral for quantum mechanics onthe group by using a non-commutative dual space representation obtained throughthe transform. Possible advantages of the formalism include: (1) The transformprovides an alternative to the spectral decomposition via representation theoryof Lie groups and the use of special functions. (2) The non-commutative dualvariables are physically more intuitive, since despite the non-commutativitythey are analogous to the corresponding classical variables. The work isexpected, among other possible applications, to allow for the metricrepresentation of Lorentzian spin foam models in the context of quantumgravity.

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