Global spinor fields in space--time

Journal Article · Sat Dec 01 04:00:00 EST 1973 · Gen. Relativity Gravitation, v. 4, no. 6, pp. 421-433

DOI:https://doi.org/10.1007/BF01215402· OSTI ID:4331298

Lee, K K

Space-time manifolds that are space- and time-oriented, causal, and possess spinor structures are considered. Five propositions are proven: if a connected, space- and time-oriented manifold is simply connected, then it is noncompact; if such a manifold is simply connected, it admits a spinor structure, which, moreover, is unique; if the space-like section of M is compact, then there exists a global system of orthonormal tetrads on M; the necessary and sufficient condition for every space-time M whose space-like section is compact to admit a spinor structure is that M have a global system of orthonormal tetrads; every space-time M which can be embedded in R/sup 6/ admits a spinor structure. It is further suggested that in view of the fact that the existence of a spinor structure is related to homotopy properties, space-time manifolds may be classified in terms of their homotopy groups pi /sub i/(M), i = 1, 2, 3, 4. In a concluding section, some avenues for future research are discussed. (auth)

• Research Organization: Syracuse Univ., NY
• NSA Number: NSA-29-019997
• OSTI ID: 4331298
• Journal Information: Gen. Relativity Gravitation, v. 4, no. 6, pp. 421-433, Journal Name: Gen. Relativity Gravitation, v. 4, no. 6, pp. 421-433; ISSN GRGVA
• Country of Publication: United Kingdom
• Language: English

Related Subjects

*QUANTUM FIELD THEORY-- SPACE-TIME
CAUSALITY
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SPINORS