Twistors and induced representations of SU(2,2)

Journal Article · Thu Sep 01 04:00:00 EDT 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523494· OSTI ID:7319152

Lerner, D E

We give an explicit realization of a series of representations of SU(2,2) induced by R/sup +/ + SL(2,C). Vectors in these representation spaces are homogeneous spinor-valued functions of two twistor variables. They may also be realized, in a frame-dependent way, either as conformally invariant fields in Minkowski space or as homogeneous spinor-valued functions on the O(2,4) null cone. The conformal invariance of the massless free fields is discussed from this point of view, and the twistor version of the field equations is derived. Finally, irreducible twistors are shown to correspond to conformally invariant fields satisfying the generalized twistor equation.

• Research Organization: University of Kansas, Lawrence, Kansas 66045
• OSTI ID: 7319152
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 18:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL SPACE
MINKOWSKI SPACE
RELATIVITY THEORY
SL GROUPS
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TWISTOR THEORY