Higher-Stage Noether Identities and Second Noether Theorems
The direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higher-stage Noether identities which is descri...
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2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/127481 |
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| author | G. Sardanashvily |
| author_facet | G. Sardanashvily |
| author_sort | G. Sardanashvily |
| collection | DOAJ |
| description | The direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higher-stage Noether identities which is described in the homology terms. If a certain homology regularity condition holds, one can associate with a reducible degenerate Lagrangian the exact Koszul–Tate chain complex possessing the boundary operator whose nilpotentness is equivalent to all complete nontrivial Noether and higher-stage Noether identities. The second
Noether theorems associate with the above-mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher-order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above-mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian. |
| format | Article |
| id | doaj-art-9f5687b1bd16479fae33d7165ef13745 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-9f5687b1bd16479fae33d7165ef137452025-02-03T06:43:47ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/127481127481Higher-Stage Noether Identities and Second Noether TheoremsG. Sardanashvily0Department of Theoretical Physics, Moscow State University, Moscow 119999, RussiaThe direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higher-stage Noether identities which is described in the homology terms. If a certain homology regularity condition holds, one can associate with a reducible degenerate Lagrangian the exact Koszul–Tate chain complex possessing the boundary operator whose nilpotentness is equivalent to all complete nontrivial Noether and higher-stage Noether identities. The second Noether theorems associate with the above-mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher-order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above-mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian.http://dx.doi.org/10.1155/2015/127481 |
| spellingShingle | G. Sardanashvily Higher-Stage Noether Identities and Second Noether Theorems Advances in Mathematical Physics |
| title | Higher-Stage Noether Identities and Second Noether Theorems |
| title_full | Higher-Stage Noether Identities and Second Noether Theorems |
| title_fullStr | Higher-Stage Noether Identities and Second Noether Theorems |
| title_full_unstemmed | Higher-Stage Noether Identities and Second Noether Theorems |
| title_short | Higher-Stage Noether Identities and Second Noether Theorems |
| title_sort | higher stage noether identities and second noether theorems |
| url | http://dx.doi.org/10.1155/2015/127481 |
| work_keys_str_mv | AT gsardanashvily higherstagenoetheridentitiesandsecondnoethertheorems |