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International Journal of Applied Mathematics and Theoretical Physics

Anyons in Three Dimensions with Geometric Algebra

Alexander Soiguine

Published Sep 5, 2016• 0 citations
Publisher

Abstract

Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. Could this be the result of a wrong mathematical structure providing inadequate understanding of the quantum phenomena [1]? Part of the problem is that the terms “state”, “observable”, “measurement” require a clear unambiguous definition that will make them universally acceptable in both classical and quantum mechanics. This concrete definition will help to further develop a feasible formalism for the challenging area of quantum computing [2].

DOI
10.11648/j.ijamtp.20160203.11

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Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. Could this be the result of a wrong mathematical structure providing inadequate understanding of the quantum phenomena [1]? Part of the problem is that the terms “state”, “observable”, “measurement” require a clear unambiguous definition that will make them universally acceptable in both classical and quantum mechanics. This concrete definition will help to further develop a feasible formalism for the challenging area of quantum computing [2].
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The Geometric Algebra formalism opens the door to developing a theory replacing conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions, followed by unambiguous definition of states, observables, measurements, bring into reality clear explanations of some weird quantum mechanical features, particularly, the results of double-slit experiments where particles create diffraction patterns inherent to a wave, or modeling atoms as a kind of solar system.
The Geometric Algebra formalism opens the door to developing a theory upgrading conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions; unambiguous definition of states, observables, measurements bring into reality clear explanations of conventional weird quantum mechanical features, particularly the results of double split experiments where particles create diffraction patterns inherent to wave diffraction. This weirdness of the double split experiment is milestone of all further difficulties in interpretation of quantum mechanics.