The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Abstract
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularisation parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularisation of short distance divergences, keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems.
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Cite
@article{arxiv.0908.0805,
title = {The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator},
author = {Jan Govaerts and Calvin Matondo Bwayi and Olivier Mattelaer},
journal= {arXiv preprint arXiv:0908.0805},
year = {2015}
}
Comments
18 pages