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].
| Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 3) |
| DOI | 10.11648/j.ijamtp.20160203.11 |
| Page(s) | 21-27 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Anyons, States, Observables, Measurements, Quantum Computing, Geometric Algebra
| [1] | B. J. Hiley, "Structure Process, Weak Values and Local Momentum," Journal of Physics: Conference Series, vol. 701, no. 1, 2016. |
| [2] | A. Soiguine, Geometric Phase in Geometric Algebra Qubit Formalism, Saarbrucken: LAMBERT Academic Publishing, 2015. |
| [3] | J. Bell, "On the problem of hidden variables in quantum theory," Rev. Mod. Phys., vol. 38, pp. 447-452, 1966. |
| [4] | S. Kochen and E. P. Specker, "The problem of hidden variables in quantum mechanics," J. Math. Mech., vol. 17, pp. 59-88, 1967. |
| [5] | P. A. M. Dirac, "A new notation for quantum mechanics," Mathematical Proceedings of the Cambridge Philosophical Society, vol. 35, no. 3, pp. 416-418, 1939. |
| [6] | A. M. Soiguine, "Complex Conjugation - Relative to What?," in Clifford Algebras with Numeric and Symbolic Computations, Boston, Birkhauser, 1996, pp. 284-294. |
| [7] | A. Soiguine, "What quantum "state" really is?," June 2014. [Online]. Available: http://arxiv.org/abs/1406.3751. |
| [8] | A. Soiguine, "Geometric Algebra, Qubits, Geometric Evolution, and All That," January 2015. [Online]. Available: http://arxiv.org/abs/1502.02169. |
| [9] | C. E. Rowell, "An Invitation to the Mathematics of Topological Quantum Computation," Journal of Physics: Conference Series, vol. 698, 2016. |
| [10] | A. Soiguine, Vector Algebra in Applied Problems, Leningrad: Naval Academy, 1990 (in Russian). |
| [11] | K. Y. Bliokh, A. Y. Bekshaev, A. G. Kofman and F. Nori, "Photon trajectories, anomalous velocities and weak measurements: a classical interpretation," New Journal of Physics, vol. 15, 2013. |
APA Style
Alexander Soiguine. (2016). Anyons in Three Dimensions with Geometric Algebra. International Journal of Applied Mathematics and Theoretical Physics, 2(3), 21-27. https://doi.org/10.11648/j.ijamtp.20160203.11
ACS Style
Alexander Soiguine. Anyons in Three Dimensions with Geometric Algebra. Int. J. Appl. Math. Theor. Phys. 2016, 2(3), 21-27. doi: 10.11648/j.ijamtp.20160203.11
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Download@article{10.11648/j.ijamtp.20160203.11,
author = {Alexander Soiguine},
title = {Anyons in Three Dimensions with Geometric Algebra},
journal = {International Journal of Applied Mathematics and Theoretical Physics},
volume = {2},
number = {3},
pages = {21-27},
doi = {10.11648/j.ijamtp.20160203.11},
url = {https://doi.org/10.11648/j.ijamtp.20160203.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160203.11},
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].},
year = {2016}
}
TY - JOUR T1 - Anyons in Three Dimensions with Geometric Algebra AU - Alexander Soiguine Y1 - 2016/09/05 PY - 2016 N1 - https://doi.org/10.11648/j.ijamtp.20160203.11 DO - 10.11648/j.ijamtp.20160203.11 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 21 EP - 27 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20160203.11 AB - 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]. VL - 2 IS - 3 ER -
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