Conformally Invariant Operators of Standard Type

Conformally invariant non-local operators

“…Since null geodesics depend only on conformal structure, the classical field equations describing massless particles, for example the Maxwell and Dirac (neutrino) equations, can be expected to depend only on conformal structure [4,20]. In recent years, much work has been done on the systematic construction, understanding, and classification of conformally invariant differential operators [2,3,6,7,21,23,28,30,31,41,45,47]. In the light of string theory and other recent developments [19], the importance of such operators, even beyond those familiar from earlier physical investigations, has been underlined.…”

On Conformal Invariants Built from Spinor Fields

“…There is an extensive literature on conformally invariant differential operators for tensor and spinor fields ( see e. g. [Bas1,Bas2,BaE,BEG,BEGr,Br1,Br2,BØ,ER,Go1,Go2,Gr,GJMS,PR,S,W3]). These have a great variety of applications, e. g. in the representation theory of the conformal group C(M, g) (see e.g.…”

“…These have a great variety of applications, e. g. in the representation theory of the conformal group C(M, g) (see e.g. [Br1,Br2,BØ,BEGr]), in the "conformal extension" of the heat equation [BØ], in connection with the twistor theory (see e. g. [PR,BaE,BEG,Go2]), on Huygens' principle [CM,Gü,McL,W3]) and in zero -mass field equations [PR,I,W3].…”

“…Systematic investigations have been carried out in the recent years [Bas1,Bas2,BE,BaE,BØ,Br1,Br2,E,ER,FG,G,GJMS,GeW1,GeW2,Go1,Go2,GW1,GW2,PR,S,W1,W2]. They were inspired very much by Penrose's twistor theory.…”

“…The existence of the operators described in the Propositions 5.1 and 5.4 is due to Eastwood and Rice [ER]. Explicit formulae for these operators are also available via Gover's method [Go2]. They are standard operators of Gover's Proposition 5.6.…”