Implications of minimum‐length deformed quantum mechanics for QFT/QG

Maziashvili, Michael

doi:10.1002/prop.201200139

Cited by 13 publications

(13 citation statements)

References 61 publications

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“…Simple physical picture behind this consideration allows one to guess higher-dimensional generalization of minimum-length deformed quantum mechanics (QM). The deformed QM derived this way disagrees with the result that follows from the well known arguments [4][5][6] (and some other closely related arguments [7]) for estimating the gravitational corrections to the uncertainty relation. The rest of the paper is devoted to the * Electronic address: maziashvili@iliauni.edu.ge discussion of quantum field theory (QFT) in view of the deformed quantization both at first and second quantization levels.…”

Section: A Introductioncontrasting

confidence: 65%

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Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

Maziashvili

2015

Phys. Rev. D

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In contrast to the 3D case, different approaches for deriving the gravitational corrections to the Heisenberg uncertainty relation do not lead to the unique result whereas additional spatial dimensions are present in the theory. We suggest to take logarithmic corrections to the black hole entropy, which has recently been proved both in string theory and loop quantum gravity to persist in presence of additional spatial dimensions, as a point of entry for identifying the modified Heisenberg-Weyl algebra. We then use a particular Hilbert space representation for such a quantum mechanics to construct the correspondingly modified field theory and address some phenomenological issues following from it. Some subtleties arising at the second quantization level are clearly pointed out. Solving the field operator to the first order in deformation parameter and defining the modified wave function for a free particle, we discuss the possible phenomenological implications for the black hole evaporation. Putting aside modifications arising at the second quantization level, we address the corrections to the gravitational potential due to modified propagator (back reaction on gravity) and see that correspondingly modified Schwarzschild-Tangherlini space-time shows up the disappearance of the horizon and vanishing of surface gravity when black hole mass approaches the quantum gravity scale. This result points out to the existence of zero-temperature black hole remnants.

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Section: A Introductioncontrasting

confidence: 65%

“…In the case δP ≪ G −1/(2+n) N the correction term in Eq. (16) can be considered as a result of the gravitational extension of the wave-packet localization width as compared to the Minkowskian background [7]. Yet, the correction term in Eq.…”

Section: Comparing With the Results Following Frommentioning

confidence: 99%

Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

Maziashvili

2015

Phys. Rev. D

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“…Any phenomenological modifications to the standard UP, motivated by such heuristic considerations as the disturbance to the quantum mechanical system caused by the gravitational field of the probing particle, must be checked for mathematical consistency. This may be possible using theories of deformed quantum mechanics, in which the deformation parameter is explicitly linked to a change in the background metric [12,16,17]. However, it remains unclear whether any GUP-type phenomenology which leads to a unified expression for the Compton and Schwarzschild scales can account for their different physical natures.…”

Section: Discussionmentioning

confidence: 99%

“…[12]). Such a theory can be consistently formulated in terms of a vector space [13,14,15] and may incorporate quantum gravity effects if the GUP deformations are directly related to deformations of the metric [16,17]. However, this is not the approach adopted here.…”

Section: Between Measurements the Development Of The Wave Function Wmentioning

confidence: 99%

The Compton-Schwarzschild correspondence from extended de Broglie relations

Lake

Carr

2015

J. High Energ. Phys.

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The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classical gravity. In a mass-radius diagram, the two lines intersect near the Planck point (l P , m P ), where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near (l P , m P ). It is unclear what physical interpretation can be given to quantum particles with energy E m P c 2 , since they correspond to wavelengths λ l P or time periods τ t P in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schrödinger equation and a modified expression for the Compton wavelength, which may be extended into the region E m P c 2 . For the proposed modification, we recover the expression for the Schwarzschild radius for E m P c 2 and the usual Compton formula for E m P c 2 . The sign of the inequality obtained from the uncertainty principle reverses at m ≈ m P , so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the selfgravitation of the wave packet.

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“…Therefore, the corresponding ( + 1)-dimensional deformed commutation relations are not Lorentz invariant and give rise to some version of the deformed special relativity. The field theories built on such commutation relations hence do not respect Lorentz symmetry [15,[18][19][20]. Although Lorentz invariance is not required for the generalization, there are some attempts to introduce ( +1)-dimensional deformed Lorentz invariant generalizations of -dimensional deformed commutation relations [21,22].…”

Section: Introductionmentioning

confidence: 99%

Covariant GUP Deformed Hamilton-Jacobi Method

Wang

Yang

2017

Advances in High Energy Physics

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We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action of tunneling of a fermionic particle from a charged black hole can be written in the same form of that for a scalar particle. On the other hand, various theories of quantum gravity suggest the existence of a minimal length scale, incorporating of which into quantum mechanics implies a modification of the uncertainty principle. In the scenario incorporating the generalized uncertainty principle (GUP) into a quantum field theory (QFT) in a covariant way, we derive the deformed model-independent KG/Dirac and Hamilton-Jacobi equations using the methods of effective field theory. For this Lorentz invariant GUP modified QFT, we find that the effect of GUP on the Hamilton-Jacobi equations is simply to "renormalize" the mass of the emitted particles, from to eff . Therefore, in this scenario, the Hawking temperature of a black hole does not receive any corrections from the GUP effect.

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Implications of minimum‐length deformed quantum mechanics for QFT/QG

Cited by 13 publications

References 61 publications

Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

The Compton-Schwarzschild correspondence from extended de Broglie relations

Covariant GUP Deformed Hamilton-Jacobi Method

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