# Hilbert space representation of maximal length and minimal momentum uncertainties

@inproceedings{Amouzouvi2021HilbertSR, title={Hilbert space representation of maximal length and minimal momentum uncertainties}, author={Kossi Amouzouvi and Benjamin Appiah and Lat{\'e}vi M. Lawson and Abdel-Baset A. Mohamed}, year={2021} }

Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys. Rev. D 95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle’s horizon or cosmic topology. Following this work, we propose a new deformed algebra and derive the maximal length uncertainty and its corresponding minimal momentum uncertainty from the generalized uncertainty principle. We construct a Hilbert space…

## Figures from this paper

## References

SHOWING 1-10 OF 41 REFERENCES

Minimal length, maximal momentum and Hilbert space representation of quantum mechanics

- Physics
- 2012

Kempf et al. in Ref. [A. Kempf, G. Mangano, and R. B. Mann, Phys. Rev. D 52, 1108 (1995).] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length.…

A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications

- Physics
- 2012

Abstract In a recent paper, we presented a nonperturbative higher order Generalized Uncertainty Principle (GUP) that is consistent with various proposals of quantum gravity such as string theory,…

Generalized space and linear momentum operators in quantum mechanics

- Physics, Mathematics
- 2013

We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum…

On the two new types of the higher order GUP with minimal length uncertainty and maximal momentum

- Physics
- 2017

Abstract In this letter, we present two new types of D -dimensional nonperturbative Generalized Uncertainty Principle (GUP) which are predicted both a minimal length uncertainty and a maximal…

On nonlocality, lattices and internal symmetries

- Physics
- 1997

We study functional analytic aspects of two types of correction terms to the Heisenberg algebra. One type of correction terms is known to induce a finite lower bound Δx0 to the resolution of…

A higher order GUP with minimal length uncertainty and maximal momentum

- Physics
- 2012

Abstract We present a higher order generalized (gravitational) uncertainty principle (GUP) in the form [ X , P ] = i ℏ / ( 1 − β P 2 ) . This form of GUP is consistent with various proposals of…

Noncommutative geometric regularization.

- Physics, MedicinePhysical review. D, Particles and fields
- 1996

In a path integral approach to the formulation of field theories on noncommutative geometries, it is generally proved that IR regularization can be generally proved for the case of noncommuter geometry which imply minimal uncertainties in momenta.

Position-dependent mass in strong quantum gravitational background fields

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant…

On the thermodynamics of relativistic ideal gases in the presence of a maximal length

- Physics
- 2020

Abstract We investigate the thermostatistics of relativistic ideal gases within the recently proposed deformed Heisenberg algebra (Perivolaropoulos, 2017), which includes a maximal length. By using…

Hilbert space representation of the minimal length uncertainty relation.

- Physics, MedicinePhysical review. D, Particles and fields
- 1995

The quantum mechanical structure which underlies the generalized uncertainty relation which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements is studied.