Jan Govaerts et al 2009 J. Phys. A: Math. Theor. 42 445304 doi:10.1088/1751-8113/42/44/445304
The Klauder–Daubechies construction of the phase-space path integral and the harmonic oscillator
Jan Govaerts1,2,5, Calvin Matondo Bwayi3 and Olivier Mattelaer1,4
Show affiliationsThe canonical operator quantization 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 regularization parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularization of short distance divergences, keeping a finite value for that time scale offers some tantalizing prospects when it comes to strong gravitational quantum systems.
- PACS
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03.65.Ge Solutions of wave equations: bound states
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
81S40 Path integrals (See also 58D30)
81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 44 (6 November 2009)
Received 6 August 2009
Published 16 October 2009
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The Klauder–Daubechies construction of the phase-space path integral and the harmonic oscillator
Jan Govaerts et al 2009 J. Phys. A: Math. Theor. 42 445304
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