Product associativity in scator algebras and the quantum wave function collapse

Manuel Fernandez-guasti

doi:10.32323/ujma.423045

EN

Product associativity in scator algebras and the quantum wave function collapse

Abstract

The scator product in $1+n$ dimensions for $n>1$, is associative if all possible product pairs have a non vanishing additive scalar component. The product is in general, not associative in the additive representation whenever the additive scalar component of a product pair is zero. A particular case of this statement is non associativity due to zero products of non zero factors. These features of scator algebra could be used to model the quantum wave function evolution and collapse in a unified description.

Keywords

Commutative algebras,Hypercomplex numbers,Non associative algebras,Quantum measurement problem

References

[1] M. Fernández-Guasti. A non-distributive extension of complex numbers to higher dimensions. Adv. Appl. Clifford Algebras, 25:829–849, Oct. 2015.
[2] A. Kobus and J. L. Cieśliński. On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions. Advances in Applied Clifford Algebras,27(2):1369–1386, 2017.
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[4] M. Fernández-Guasti and F. Zaldívar. Multiplicative representation of a hyperbolic non distributive algebra. Adv. Appl. Clifford Algebras, 24(3):661–674,2014.
[5] M. Fernández-Guasti and F. Zaldívar. An elliptic non distributive algebra. Adv. Appl. Clifford Algebras, 23(4):825–835, 2013.
[6] W. E. Baylis and J. D. Keselica. A classical spinor approach to the quantum/classical interface. Canadian Journal of Physics, 86(4):629–634, 2008.
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[8] F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti, and P. Zampetti. The Mathematics of Minkowski Space-Time. Number 2 in Frontiers inMathematics. Birkhauser Verlag, 2008.
[9] M. Fernández-Guasti. Time and space transformations in a scator deformed Lorentz metric. European Physical Journal - Plus, 129(195):1–10, 2014.
[10] M. Fernández-Guasti and F. Zaldívar. Hyperbolic superluminal scator algebra. Adv. Appl. Clifford Algebras, 25(2):321–335, 2015.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Manuel Fernandez-guasti ^*
0000-0002-1839-6002
Mexico

Publication Date

June 26, 2018

Submission Date

May 12, 2018

Acceptance Date

June 21, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

DOI

https://doi.org/10.32323/ujma.423045

IZ

https://izlik.org/JA65BB33EG

APA

Fernandez-guasti, M. (2018). Product associativity in scator algebras and the quantum wave function collapse. Universal Journal of Mathematics and Applications, 1(2), 80-88. https://doi.org/10.32323/ujma.423045

AMA

1.Fernandez-guasti M. Product associativity in scator algebras and the quantum wave function collapse. Univ. J. Math. Appl. 2018;1(2):80-88. doi:10.32323/ujma.423045

Chicago

Fernandez-guasti, Manuel. 2018. “Product Associativity in Scator Algebras and the Quantum Wave Function Collapse”. Universal Journal of Mathematics and Applications 1 (2): 80-88. https://doi.org/10.32323/ujma.423045.

EndNote

Fernandez-guasti M (June 1, 2018) Product associativity in scator algebras and the quantum wave function collapse. Universal Journal of Mathematics and Applications 1 2 80–88.

IEEE

[1]M. Fernandez-guasti, “Product associativity in scator algebras and the quantum wave function collapse”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 80–88, June 2018, doi: 10.32323/ujma.423045.

ISNAD

Fernandez-guasti, Manuel. “Product Associativity in Scator Algebras and the Quantum Wave Function Collapse”. Universal Journal of Mathematics and Applications 1/2 (June 1, 2018): 80-88. https://doi.org/10.32323/ujma.423045.

JAMA

1.Fernandez-guasti M. Product associativity in scator algebras and the quantum wave function collapse. Univ. J. Math. Appl. 2018;1:80–88.

MLA

Fernandez-guasti, Manuel. “Product Associativity in Scator Algebras and the Quantum Wave Function Collapse”. Universal Journal of Mathematics and Applications, vol. 1, no. 2, June 2018, pp. 80-88, doi:10.32323/ujma.423045.

Vancouver

1.Manuel Fernandez-guasti. Product associativity in scator algebras and the quantum wave function collapse. Univ. J. Math. Appl. 2018 Jun. 1;1(2):80-8. doi:10.32323/ujma.423045