A Cohomological Description of Massive Fields

Hughston, L P and Hurd, T R. 1981. A Cohomological Description of Massive Fields. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 378(1772), pp. 141-154. ISSN 0080-4630 [Article]

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Abstract or Description

In this paper we present a generalization of the theory of the P-transform that encompasses the n-twistor description of massive fields. Attention is devoted to the two-twistor description, for which it is shown that the cohomology group H2(P+3 x P+3, Om, s ( — ξ — 2, — ŋ — 2)) is naturally isomorphic to the space of positive-frequency free fields of mass m and spin s, provided s — 1/2 | ξ — ŋ| is a non-negative integer, and vanishes otherwise. The sheaf Om, s( — ξ — 2, —ŋ — 2) is a subsheaf of the standard sheaf of twisted holomorphic functions O( — ξ — 2, — ŋ — 2) on P+3 x P+3 and satisfies a pair of differential equations determining the mass and the spin. In establishing these results extensive use is made of a certain class of two-point fields on space-time, required to be of positive frequency and of zero rest mass in each variable separately, and also subject to a condition of definite total mass and total spin. Such fields are of considerable interest in their own right, for example in connection with the theory of twistor diagrams, and in this paper we formulate a number of their basic properties.

Item Type:

Article

Identification Number (DOI):

https://doi.org/10.1098/rspa.1981.0145

Departments, Centres and Research Units:

Computing

Dates:

DateEvent
11 September 1981Published

Item ID:

31604

Date Deposited:

14 Mar 2022 12:49

Last Modified:

14 Mar 2022 12:49

Peer Reviewed:

Yes, this version has been peer-reviewed.

URI:

https://research.gold.ac.uk/id/eprint/31604

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