| Title:
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Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields (English) |
| Author:
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Canarutto, Daniel |
| Language:
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English |
| Journal:
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Archivum Mathematicum |
| ISSN:
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0044-8753 (print) |
| ISSN:
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1212-5059 (online) |
| Volume:
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54 |
| Issue:
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4 |
| Year:
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2018 |
| Pages:
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205-226 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
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An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle $SM$ with 2-dimensional fibers, called a $2$-spinor bundle. Any further considered object is assumed to be a dynamical field; these include the gravitational field, which is jointly represented by a soldering form (the tetrad) relating the tangent space $M$ to the $2$-spinor bundle, and a connection of the latter (spinor connection). The Lie derivatives of objects of all considered types, with respect to a vector field ${\scriptstyle X}\colon M\rightarrow M$, turn out to be well-defined without making any special assumption about ${\scriptstyle X}$, and fulfill natural mutual relations. (English) |
| Keyword:
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Lie derivatives of spinors |
| Keyword:
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Lie derivatives of spinor connections |
| Keyword:
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deformed tetrad gravity |
| MSC:
|
53B05 |
| MSC:
|
58A32 |
| MSC:
|
83C60 |
| idZBL:
|
Zbl 06997351 |
| idMR:
|
MR3887361 |
| DOI:
|
10.5817/AM2018-4-205 |
| . |
| Date available:
|
2018-12-06T16:08:31Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147498 |
| . |
| Reference:
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