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Register a new userAnyons Live in Non-Commutative Space: A First Principles Demonstration
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In this paper we have successfully established (from first principles) that anyons do live in a 2-dimensional {it{noncommutative}} space. We have directly computed the non-trivial uncertainty relation between anyon coordinates, ${sqrt{Delta x^2Delta y^2}}=Thetasigma$, using the recently constructed anyon wave function [J. Majhi, S. Ghosh and S.K. Maiti, Phys. Rev. Lett. textbf{123}, 164801 (2019)] cite{jan}, in the framework of I. Bialynicki-Birula and Z. Bialynicka-Birula, New J. Phys. textbf{21}, 07306 (2019) cite{bel}. Furthermore we also compute the Heisenberg uncertainty relation for anyon and as a consistency check, show that the results of cite{bel} prove that, as expected, electrons live in 3-dimensional commutative space.
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