Free Motion of a Dirac Particle with a Minimum Uncertainty in Position

Arman Shokrollahi

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Free Motion of a Dirac Particle with a Minimum Uncertainty in Position

Arman Shokrollahi

General Relativity and Quantum Cosmology · Submitted 2 Aug 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.05 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances. Then, we introduce a new representation for coordinate and momentum operators which leads to a generalized Dirac equation. The solutions of the generalized Dirac equation for a free particle will be explicitly obtained. We also obtain the modified fermionic propagator for a free Dirac particle.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters.	contribution 0.91	0.91	0.07	asserted 1.00
s1	Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances.	result 0.91	0.91	0.39	asserted 0.98
s2	Then, we introduce a new representation for coordinate and momentum operators which leads to a generalized Dirac equation.	method 0.75	0.95	0.08	asserted 1.00
s3	The solutions of the generalized Dirac equation for a free particle will be explicitly obtained.	result 0.59	0.86	0.17	asserted 0.98
s4	We also obtain the modified fermionic propagator for a free Dirac particle.	result 0.86	0.95	0.15	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances. Then, we introduce a new representation for coordinate and momentum operators which leads to a generalized Dirac equation. The solutions of the generalized Dirac equation for a free particle will be explicitly obtained. We also obtain the modified fermionic propagator for a free Dirac particle.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Compares with 2 papers

Particularly, it has been reduced to the Snyder algebra (for more details see [ref] ).

Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator · Lorentz covariant deformed algebra · 0.89
Particularly, it has been reduced to the Snyder algebra (for more details see [ref] ).

Lorentz-covariant deformed algebra with minimal length · Lorentz covariant deformed algebra · 0.89

Cites as background 9 papers

Kempf has expanded the studies on the structure of space-time at the Planck scale [ref] .

On the Structure of Space-Time at the Planck Scale · Introduction · 0.95
Kempf has expanded the studies on the structure of space-time at the Planck scale [ref] .

Hilbert Space Representation of the Minimal Length Uncertainty Relation · Introduction · 0.95
The modification of the Heisenberg algebra and its extension to higher dimensions through GUP has been extensively studied recently (for more details see [ref] ).

Minimal Length Uncertainty Relation and gravitational quantum well · Introduction · 0.96

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