Pauli's theorem in Clifford algebras of odd dimension
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 1, pp. 44-61
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Pauli's theorem is investigated in real Clifford algebras of odd dimension. In Clifford algebras $R_{3,0}$ and $R_{5,0}$ an algorithm for constructing the Pauli operator is given. This algorithm is transferred to an arbitrary Clifford algebra of odd dimension $R_{p,q+1}$ ($R_{p+1,q}$). An iterative formula for finding the Pauli operator is obtained. It is shown that the problem of constructing the Pauli operator is related to the problem of zero divisors in Clifford algebras. When constructing Pauli operators, two types of conjugations are used: Clifford conjugation and reverse conjugation. If $p+q+1\equiv 3 \pmod 4$, then when constructing the Pauli operator Clifford conjugation is used; if $p+q+1\equiv 1 \pmod 4$ then reverse conjugation is used.
Keywords:
odd Clifford algebras, Pauli theorem, zero divisors.
@article{VUU_2022_32_1_a3,
author = {S. P. Kuznetsov and V. V. Mochalov and V. P. Chuev},
title = {Pauli's theorem in {Clifford} algebras of odd dimension},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {44--61},
publisher = {mathdoc},
volume = {32},
number = {1},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_1_a3/}
}
TY - JOUR AU - S. P. Kuznetsov AU - V. V. Mochalov AU - V. P. Chuev TI - Pauli's theorem in Clifford algebras of odd dimension JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2022 SP - 44 EP - 61 VL - 32 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2022_32_1_a3/ LA - ru ID - VUU_2022_32_1_a3 ER -
%0 Journal Article %A S. P. Kuznetsov %A V. V. Mochalov %A V. P. Chuev %T Pauli's theorem in Clifford algebras of odd dimension %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2022 %P 44-61 %V 32 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2022_32_1_a3/ %G ru %F VUU_2022_32_1_a3
S. P. Kuznetsov; V. V. Mochalov; V. P. Chuev. Pauli's theorem in Clifford algebras of odd dimension. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 1, pp. 44-61. http://geodesic.mathdoc.fr/item/VUU_2022_32_1_a3/