×

Hidden nonassociative structure in supersymmetric quantum mechanics. (English) Zbl 1201.81062

The paper under review considers an associative \(\mathbb G\) (algebra of observables) of a nonassociative algebra \(\mathbb A\). In this way, the Hamilton equations then allow to formulate quantum dynamics for operators \(L\in\mathbb G\), using nonassociative elements \(h_1,h_2\in\mathbb A\setminus\mathbb G\). Thus, the author shows that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.

MSC:

81Q60 Supersymmetry and quantum mechanics
47E05 General theory of ordinary differential operators
47L70 Nonassociative nonselfadjoint operator algebras
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
11R52 Quaternion and other division algebras: arithmetic, zeta functions
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Jordan, Ann. Math. 35 pp 29– (1934)
[2] Zelmanov, Siberian Math. J. 24 pp 89– (1983)
[3] Dzhunushaliev, J. Gen. Lie Theory Appl. 2(4) pp 269– (2008)
[4] S. Okubo
[5] Myung, Trans. Am. Math. Soc. 167 pp 79– (1972)
[6] Dzhunushaliev, J. Math. Phys. 49 pp 042108– (2008)
[7] Haymaker, Am. J. Phys. 54 pp 928– (1986)
[8] Witten, Nucl. Phys. B 188 pp 513– (1981)
[9] Cooper, Ann. Phys. 146 pp 262– (1983)
[10] Gunaydin, J. Math. Phys. 14 pp 1651– (1973)
[11] Carmody, Appl. Math. Comput. 28 pp 47– (1988)
[12] Carmody, Appl. Math. Comput. 84 pp 27– (1997)
[13] Kuznetsova, JHEP, J. High Energy Phys. 0603 pp 098– (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.