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

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

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE8C-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE8D-2
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1111.6481 (Preprint), 131KB
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 Creators:
Raasakka, Matti1, Author              
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1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:67201              

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Free keywords: Mathematical Physics, math-ph,General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP
 Abstract: 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.

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 Dates: 2011-11-282011-12-12
 Publication Status: Not specified
 Pages: 7 pages, correction to the applicability of coordinates plus other minor corrections
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1111.6481
URI: http://arxiv.org/abs/1111.6481
 Degree: -

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