A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F09%3A00034160" target="_blank" >RIV/00216224:14310/09:00034160 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
Original language description
We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger--Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth--order term proportional to the Levi--Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann--odd, second--order Delta operator in antisymplectic geometry, which in general has a zeroth--order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two--loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Physics
ISSN
0022-2488
e-ISSN
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Volume of the periodical
2009
Issue of the periodical within the volume
50 073504
Country of publishing house
US - UNITED STATES
Number of pages
51
Pages from-to
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UT code for WoS article
000268614500023
EID of the result in the Scopus database
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