{"title":"Uncertainty relations for the relativistic Jackiw-Nair nyon: A first principles derivation","authors":"Joydeep Majhi, Subir Ghosh","doi":"10.1209/0295-5075/ad0670","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we have explicitly computed the $position-position$ and $position-momentum$ (Heisenberg) Uncertainty Relations for the model of relativistic particles with arbitrary spin, proposed by Jackiw and Nair \\cite{jn} as a model for Anyon, in a purely quantum mechanical framework. This supports (via Schwarz inequality) the conjecture that anyons live in a 2-dimensional {\\it{noncommutative}} space. We have computed the non-trivial uncertainty relation between anyon coordinates, ${\\sqrt{\\Delta x^2\\Delta y^2}}=\\hbar\\bar{\\Theta}_{xy}$, using the recently constructed anyon wave function \\cite{jan}, in the framework of \\cite{bel}. We also compute the Heisenberg (position-momentum) uncertainty relation for anyons. Lastly we show that the identical {\\it{formalism}} when applied to electrons, yield a trivial position uncertainty relation, consistent with their living in a 3-dimensional commutative space.","PeriodicalId":11738,"journal":{"name":"EPL","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad0670","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this paper we have explicitly computed the $position-position$ and $position-momentum$ (Heisenberg) Uncertainty Relations for the model of relativistic particles with arbitrary spin, proposed by Jackiw and Nair \cite{jn} as a model for Anyon, in a purely quantum mechanical framework. This supports (via Schwarz inequality) the conjecture that anyons live in a 2-dimensional {\it{noncommutative}} space. We have computed the non-trivial uncertainty relation between anyon coordinates, ${\sqrt{\Delta x^2\Delta y^2}}=\hbar\bar{\Theta}_{xy}$, using the recently constructed anyon wave function \cite{jan}, in the framework of \cite{bel}. We also compute the Heisenberg (position-momentum) uncertainty relation for anyons. Lastly we show that the identical {\it{formalism}} when applied to electrons, yield a trivial position uncertainty relation, consistent with their living in a 3-dimensional commutative space.
期刊介绍:
General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology.
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