Quantization of Length in Spaces with Position-Dependent Noncommutativity

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Aryampilly, Jishnu, Balasundaram, Muthukumar, Rashid, Aamir
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909249000439808
author Aryampilly, Jishnu
Balasundaram, Muthukumar
Rashid, Aamir
author_facet Aryampilly, Jishnu
Balasundaram, Muthukumar
Rashid, Aamir
contents We present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl-Moyal type and Lie algebraic type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.
format Preprint
id arxiv_https___arxiv_org_abs_2309_12663
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Quantization of Length in Spaces with Position-Dependent Noncommutativity
Aryampilly, Jishnu
Balasundaram, Muthukumar
Rashid, Aamir
High Energy Physics - Theory
Mathematical Physics
Quantum Physics
We present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl-Moyal type and Lie algebraic type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.
title Quantization of Length in Spaces with Position-Dependent Noncommutativity
topic High Energy Physics - Theory
Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2309.12663