On quantum field theory with nonzero minimal uncertainties in positions and momenta

Kempf, Achim

doi:10.1063/1.531814

Cited by 173 publications

(202 citation statements)

References 51 publications

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“…For example, the ultraviolet regularity of loop graphs in such field theories has been shown. See [28,29,30]. In work by Brout et al, [11], it has been shown that this type of short-distance cut-off without energy-momentum cut-off, when built into quantum theory could resolve the transplanckian energies paradox of black hole radiation -without invoking superoscillations.…”

Section: Discussionmentioning

confidence: 99%

Black holes, bandwidths and Beethoven

Kempf

2000

Journal of Mathematical Physics

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It is usually believed that a function φ(t) whose Fourier spectrum is bounded can vary at most as fast as its highest frequency component ω max . This is in fact not the case, as Aharonov, Berry and others drastically demonstrated with explicit counter examples, so-called superoscillations. It has been claimed that even the recording of an entire Beethoven symphony can occur as part of a signal with 1Hz bandwidth. Bandlimited functions also occur as ultraviolet regularized fields. Their superoscillations have been suggested, for example, to resolve the transplanckian frequencies problem of black hole radiation.Here, we give an exact proof for generic superoscillations. Namely, we show that for every fixed bandwidth there exist functions which pass through any finite number of arbitrarily prespecified points. Further, we show that, in spite of the presence of superoscillations, the behavior of bandlimited functions can be characterized reliably, namely through an uncertainty relation: The standard deviation ∆T of samples φ(t n ) taken at the Nyquist rate obeys: ∆T ≥ 1/4ω max . This uncertainty relation generalizes to variable bandwidths. We identify the bandwidth as the in general spatially variable finite local density of the degrees of freedom of ultraviolet regularized fields.

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Section: Discussionmentioning

confidence: 99%

Black holes, bandwidths and Beethoven

Kempf

2000

Journal of Mathematical Physics

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“…These predictions motivated several authors to search for model independent arguments, leading to the same conclusions as string theory does (we refer to [16] for a survey on the subject). In particular it has been shown that the above results can be reproduced on a purely kinematical level with appropriate deformations of the Heisenberg commutation relations [49,40,33,1], i.e., of canonical quantum statistics. In all such cases the coordinates do not commute at small distances, a result which is consistent with the spirit of non-commutative geometry [7].…”

Section: Introductionmentioning

confidence: 82%

Jacobson generators, Fock representations and statistics of sl(n+1)

Palev

Jeugt

2002

Journal of Mathematical Physics

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“…The formalism, based on this deformed algebra, together with the new concepts it implies, has been discussed extensively in one and more dimensions by Kempf and co-workers in Refs. [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Pseudoharmonic oscillator in quantum mechanics with a minimal length

Bouaziz

Boukhellout

2014

Mod. Phys. Lett. A

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The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, (∆x) min = √ 5β. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration-rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules. * Electronic address: djamilbouaziz@univ-jijel.dz † Electronic address: abdelmalek-boukhellout@univ-jijel.dz

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On quantum field theory with nonzero minimal uncertainties in positions and momenta

Cited by 173 publications

References 51 publications

Black holes, bandwidths and Beethoven

Black holes, bandwidths and Beethoven

Jacobson generators, Fock representations and statistics of sl(n+1)

Pseudoharmonic oscillator in quantum mechanics with a minimal length

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