Minimal lengths in 3D via the generalized uncertainty principle
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, w...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-12-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S037026932300597X |
| _version_ | 1797454358286172160 |
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| author | Michael Bishop Joey Contreras Peter Martin Piero Nicolini Douglas Singleton |
| author_facet | Michael Bishop Joey Contreras Peter Martin Piero Nicolini Douglas Singleton |
| author_sort | Michael Bishop |
| collection | DOAJ |
| description | We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions. |
| first_indexed | 2024-03-09T15:36:04Z |
| format | Article |
| id | doaj.art-73330912b6284d93a17bf23576f465ac |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-03-09T15:36:04Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-73330912b6284d93a17bf23576f465ac2023-11-26T05:11:20ZengElsevierPhysics Letters B0370-26932023-12-01847138263Minimal lengths in 3D via the generalized uncertainty principleMichael Bishop0Joey Contreras1Peter Martin2Piero Nicolini3Douglas Singleton4Mathematics Department, California State University Fresno, Fresno, CA 93740, USAPhysics Department, California State University Fresno, Fresno, CA 93740, USAPhysics Department, California State University Fresno, Fresno, CA 93740, USADipartimento di Fisica, Università degli Studi di Trieste, Trieste, Italy; Frankfurt Institute for Advanced Studies (FIAS), Frankfurt am Main, Germany; Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität-Frankfurt am Main, Frankfurt am Main, GermanyPhysics Department, California State University Fresno, Fresno, CA 93740, USA; Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA; Corresponding author.We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.http://www.sciencedirect.com/science/article/pii/S037026932300597X |
| spellingShingle | Michael Bishop Joey Contreras Peter Martin Piero Nicolini Douglas Singleton Minimal lengths in 3D via the generalized uncertainty principle Physics Letters B |
| title | Minimal lengths in 3D via the generalized uncertainty principle |
| title_full | Minimal lengths in 3D via the generalized uncertainty principle |
| title_fullStr | Minimal lengths in 3D via the generalized uncertainty principle |
| title_full_unstemmed | Minimal lengths in 3D via the generalized uncertainty principle |
| title_short | Minimal lengths in 3D via the generalized uncertainty principle |
| title_sort | minimal lengths in 3d via the generalized uncertainty principle |
| url | http://www.sciencedirect.com/science/article/pii/S037026932300597X |
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