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@article{795295,
author = {Batalin, Igor and Bering Larsen, Klaus},
article_location = {USA},
article_number = {50 073504},
doi = {http://dx.doi.org/10.1063/1.3152575},
keywords = {Dirac Operator; Spin Representations; BV Field Antifield Formalism; Antisymplectic Geometry; Odd Laplacian},
language = {eng},
issn = {0022-2488},
journal = {Journal of Mathematical Physics},
title = {A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry},
url = {http://arxiv.org/abs/0809.4269},
volume = {2009},
year = {2009}
}
TY - JOUR
ID - 795295
AU - Batalin, Igor - Bering Larsen, Klaus
PY - 2009
TI - A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
JF - Journal of Mathematical Physics
VL - 2009
IS - 50 073504
SP - 1-51
EP - 1-51
PB - American Institute of Physics
SN - 00222488
KW - Dirac Operator
KW - Spin Representations
KW - BV Field Antifield Formalism
KW - Antisymplectic Geometry
KW - Odd Laplacian
UR - http://arxiv.org/abs/0809.4269
N2 - 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.
ER -
BATALIN, Igor a Klaus BERING LARSEN. A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry. Online. \textit{Journal of Mathematical Physics}. USA: American Institute of Physics, 2009, roč.~2009, 50 073504, s.~1-51. ISSN~0022-2488. Dostupné z: https://dx.doi.org/10.1063/1.3152575. [citováno 2024-04-24]
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