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arXiv · 0908.0805

The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator

Jan Govaerts·Calvin Matondo Bwayi·Olivier Mattelaer
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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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Jan Govaerts, Calvin Matondo Bwayi, Olivier Mattelaer. 2009-08-06. The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator. https://doi.org/10.1088/1751-8113%2F42%2F44%2F445304

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