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Speaker |
Martinetti, Pierre |
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Coauthors |
F. D'Andrea, L. Tomassini, J.-C. Wallet |
| Talk Title |
Quantum Length, Quantum Geodesics |
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Abstract |
It is a common idea that a quantum spacetime is a geometrical object in which the length is quantized. This is usually interpreted as the impossibility to measure a distance below a certain quantity, usually the Planck length. Most often this minimal length is obtained as the non-zero minimum of a suitably defined length operator, as in the Doplicher, Fredenhagen, Roberts model. On the contrary, in Connes noncommutative geometry one has a notion of distance between quantum states that can be as small as desired. At first sight this seems in contradiction with the idea of minimal length. However we will show how to quantize this distance (by doubling the spectral triple of the Moyal plane), and how this is equivalent to de-quantizing the quantum length of the DFR model. This shows that Connes spectral distance and the DFR length operator captures the same metric information, at least as long as one considers coherent states. Between eigenstates of the harmonic oscillators, there remains a difference. Our conclusion is that Connes distance and the DFR length operator make a similar proposal on how to quantize the length element, but offer distinct views on the quantization of geodesics. |
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