2009
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
BATALIN, Igor a Klaus BERING LARSENZákladní údaje
Originální název
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
Název česky
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
Autoři
BATALIN, Igor a Klaus BERING LARSEN
Vydání
Journal of Mathematical Physics, USA, American Institute of Physics, 2009, 0022-2488
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10303 Particles and field physics
Stát vydavatele
Spojené státy
Utajení
není předmětem státního či obchodního tajemství
Odkazy
Impakt faktor
Impact factor: 1.318
Označené pro přenos do RIV
Ano
Kód RIV
RIV/00216224:14310/09:00034160
Organizační jednotka
Přírodovědecká fakulta
UT WoS
Klíčová slova anglicky
Dirac Operator; Spin Representations; BV Field Antifield Formalism; Antisymplectic Geometry; Odd Laplacian
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 17. 3. 2019 17:21, doc. Klaus Bering Larsen, Ph.D.
V originále
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.
Česky
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.
Návaznosti
| MSM0021622409, záměr |
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