×

Spinors and the Dirac operator on hypersurfaces. I: General theory. (English) Zbl 0769.58055

The pin structures and the Dirac operator on hypersurfaces in the flat, Euclidean space \(\mathbb{R}^{n+1}\) are considered. It is shown that the hypersurfaces always have a pin structure and the associated bundle of Dirac or Pauli spinors is trivial. This observation is used to derive a convenient, “global” form of the Dirac operator on hypersurfaces in \(\mathbb{R}^{n+1}\).
Reviewer: V.Abramov (Tartu)

MSC:

58J05 Elliptic equations on manifolds, general theory
53C27 Spin and Spin\({}^c\) geometry
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1098/rspa.1928.0023 · JFM 54.0973.01
[2] DOI: 10.1007/BF01339504
[3] Lichnerowicz A., C. R. Acad. Sci. Paris A-B 257 pp 7– (1963)
[4] DOI: 10.1016/0001-8708(74)90021-8 · Zbl 0284.58016
[5] DOI: 10.2307/1970717 · Zbl 0164.24301
[6] DOI: 10.1007/BF02953774 · Zbl 0538.53047
[7] DOI: 10.1007/BF02953774 · Zbl 0538.53047
[8] DOI: 10.1063/1.527021 · Zbl 0599.53030
[9] Cahen M., Q. J. Pure Appl. Math. 62 pp 209– (1988)
[10] DOI: 10.1142/S0217751X86000022 · Zbl 0665.53056
[11] DOI: 10.1007/BF00401871 · Zbl 0706.58010
[12] Pauli W., Helv. Phys. Acta 12 pp 147– (1939)
[13] DeWitt-Morette C., J. Math. Phys. 41 pp 1901– (1990)
[14] DOI: 10.1017/S0305004100049410 · Zbl 0297.58008
[15] Karoubi M., Ann. Sci. Ec. Norm. Sup. 1 pp 161– (1968)
[16] DOI: 10.1007/BF00128299 · Zbl 0694.53043
[17] DOI: 10.1016/0003-4916(80)90120-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.