Polyadic Supersymmetry
We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the <i>n</i>-ary sigma matrices define...
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2025-04-01
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| author | Steven Duplij |
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| author_sort | Steven Duplij |
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| description | We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the <i>n</i>-ary sigma matrices defined in earlier work. In this way, polyadic analogs of supercharges and Hamiltonians take the cyclic shift block matrix form, and they are different from the <i>N</i>-extended and multigraded SQM. While constructing the corresponding supersymmetry as an <i>n</i>-ary Lie superalgebra (<i>n</i> is the arity of the initial associative multiplication), we have found new brackets with a reduced arity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>m</mi><mo><</mo><mi>n</mi></mrow></semantics></math></inline-formula> and a related series of <i>m</i>-ary superalgebras (which is impossible for binary superalgebras). In the case of even reduced arity <i>m</i>, we obtain a tower of higher-order (as differential operators) even Hamiltonians, while for <i>m</i> odd we obtain a tower of higher-order odd supercharges, and the corresponding algebra consists of the odd sector only. |
| format | Article |
| id | doaj-art-b0bc141305cc4c9db81abb184b065a7c |
| institution | OA Journals |
| issn | 2218-1997 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Universe |
| spelling | doaj-art-b0bc141305cc4c9db81abb184b065a7c2025-08-20T02:25:07ZengMDPI AGUniverse2218-19972025-04-0111412510.3390/universe11040125Polyadic SupersymmetrySteven Duplij0Center for Information Technology, Universität Münster, Röntgenstrasse 7-13, D-48149 Münster, GermanyWe introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the <i>n</i>-ary sigma matrices defined in earlier work. In this way, polyadic analogs of supercharges and Hamiltonians take the cyclic shift block matrix form, and they are different from the <i>N</i>-extended and multigraded SQM. While constructing the corresponding supersymmetry as an <i>n</i>-ary Lie superalgebra (<i>n</i> is the arity of the initial associative multiplication), we have found new brackets with a reduced arity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>m</mi><mo><</mo><mi>n</mi></mrow></semantics></math></inline-formula> and a related series of <i>m</i>-ary superalgebras (which is impossible for binary superalgebras). In the case of even reduced arity <i>m</i>, we obtain a tower of higher-order (as differential operators) even Hamiltonians, while for <i>m</i> odd we obtain a tower of higher-order odd supercharges, and the corresponding algebra consists of the odd sector only.https://www.mdpi.com/2218-1997/11/4/125superalgebrasuperbracketLie superalgebrasigma matrixPauli matrixarity |
| spellingShingle | Steven Duplij Polyadic Supersymmetry Universe superalgebra superbracket Lie superalgebra sigma matrix Pauli matrix arity |
| title | Polyadic Supersymmetry |
| title_full | Polyadic Supersymmetry |
| title_fullStr | Polyadic Supersymmetry |
| title_full_unstemmed | Polyadic Supersymmetry |
| title_short | Polyadic Supersymmetry |
| title_sort | polyadic supersymmetry |
| topic | superalgebra superbracket Lie superalgebra sigma matrix Pauli matrix arity |
| url | https://www.mdpi.com/2218-1997/11/4/125 |
| work_keys_str_mv | AT stevenduplij polyadicsupersymmetry |