This paper is concerned with demonstrating that the twistor realization of the ladder representation of U(p,q) can be generalized to super representations of U(p,q‖N). This is achieved by considering the generalization of twistor elementary states to a super algebraic category. Unitarity of these super representations follows from the positive definiteness of a super twistor scalar product constructed in this paper. Although generalizations of the ladder representations have been well studied by other means, it will be shown that the super twistor generalization is especially natural and merits special investigation.
REFERENCES
1.
R. J. Baston and M. G. Eastwood, The Penrose Transform—Its interaction with Representation Theory (Oxford U.P., Oxford, 1989).
2.
M. G. Eastwood, “The Generalized Twistor Transform and Unitary Representations of U(p,q),” preprint, Oxford Univ., Oxford (1983).
3.
M. G. Eastwood and A. M. Pilato, “On the Density of Twistor Elementary States,” preprint, Oxford Univ., Oxford (1985), to appear in Pacific J. Math.
4.
A. M. Pilato, “Elementary States, Supergeometry and Twistor Theory,” Ph.D. thesis, Oxford Univ. (1986).
5.
B. Kostant, “Graded Manifolds, Graded Lie Theory, and Prequantization,” in Differential Geometric Methods in Mathematical Physics, edited by K. Bleuler and A. Reetz, Lecture Notes in Mathematics Vol. 570 (Springer-Verlag, Berlin, 1977), pp. 177–306.
6.
7.
8.
S. Iitaka Algebraic Geometry. An Introduction to Birational Geometry of Algebraic Varieties (Springer-Verlag, Berlin, 1981).
9.
P. Griffiths and J. Adams, Topics in Algebraic and Analytic Geometry, Princeton Mathematical Notes, (Princeton U.P., Princeton, NJ, 1974).
10.
11.
I. R. Shafarevich, Basic Algebraic Geometry (Springer-Verlag, Berlin, 1974).
12.
Progress in Math. Vol. 36, edited by M. Artin and J. Tate (Birkhäuser, Boston, 1983).
13.
14.
15.
B. S. De Witt, Supermanifolds (Cambridge U.P., Cambridge, 1984).
16.
17.
18.
19.
20.
21.
22.
M.
Günaydin
, P.
van Nieuwenhuizer
, and N. P.
Warner
, Nucl. Phys. B
255
, 63
(1985
).23.
24.
M. Günaydin and N. P. Warner, Penn. State Univ. preprint, Nov. 1987, to appear in J. Math. Phys.
25.
26.
27.
R. Penrose, “Twistor Theory, its Aims and Achievements,” in Quantum Gravity: An Oxford Symposium, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon, Oxford, 1975), pp. 268–407.
28.
R. Penrose and W. Rindler, Spinors and Space-time (Cambridge U.P., Cambridge, Vol. I, 1984, and Vol. II, 1986).
29.
30.
31.
J.
Rawnsley
, W.
Schmid
, and J. A.
Wolf
, J. Funct. Anal.
51
, 1
(1983
).32.
33.
34.
35.
36.
37.
F. A. Berezin, The Method of Second Quantization (Academic, New York, 1973).
38.
39.
40.
This content is only available via PDF.
© 1991 American Institute of Physics.
1991
American Institute of Physics
You do not currently have access to this content.
