L};TTERE AL :NUOVO CIMENTO VOL. 19, N. 15 13 Agosto 1977 A Possible Interpretation of Theories Involving Grassmann Variables (*). A. BARDUCCI lstituto di Fisica Teorica dell'Universit& - Firenze Istituto Nazionale di Fisica Arucleare - Sezione di Firenze R. CASALBUOI~I Department o] Physics, Johns Hopkins University - Baltimore, Md 21218 Istituto Nazionale di Fisica Nucleate . Sezione di Firenze (**) L. ~USANNA Istituto .Yazionale di .Fisica Nucleate - Sezione di Firenze (ricevu~o il 20 Maggio 1977) In recent times there has been a considerable interest in theories involving anti- commuting, or Grassmann, variables. The origin of this interest comes from the dual models, where it was shown that it is possible to get graded spectrum generating algebras (1). This leads naturally to the introduction of anticommuting parameters in the theory. These antieomInuting parameters are nothing but the ~(classical ~> degrees of freedom of the fermionie string (2). These results were extended to the field theory in four dimensions by W~ss and Zvmso (a). The four-dimensional supersymmetry was first introduced by GOLFA~'D and LICHTMAN (4). Finally the combination of these ideas with the ideas of general relativity leads to supergravity (5). (*) Research supported ia part by the U.S. Energy Research and Development Administration unde Contract No. EY-76-S-02-3285. (**) Permanent address. (1) A. NEVEU and J. H. SC~IWARZ: Nucl. Phys., 31 B, 86 (1971); P. RAMOND: Phys. Rev. D, 3, 2115 (1971); J. L. GERVAIS and B. SAKITA: Nucl. Phys., 64 B, 632 (1971). (t) Y. IW&SAKI and K. EIKK&V~'A: Phys. Rev. D, 8, 440 (1973); L. N. CH&NG, K . MACR~klg and F. MA~'- SOURI: Phys. LetL, 57 B, 59 (1975). (a) J. WESS and B. ZUMINO: Nucl. Phys., 70 B, 39 (1971); see also: A. SALAMand J. STRATIIDEE: Nucl. Phys., 76 B, 477 (1974); B. ZUMINO: Proceedings o! the XKII International Con]erence on High-Energy Physics, London, 1974, (Chillon, Didcot, 1974), p. 1. (~) YU. A. GOLFAND and E. P. LICHTIvIAN : SOY. Phys. JETP LelL, 13, 452 (1971); see also: D. V. VOLKOV and V. P. ~=~KULOV: Phys. Left., 46B, 109 (1973). (~) D . Z . FI~EED.~IAN,P. V&N NIEUWENHIUZE/X Tand S. FERRARA: Phys. Rev. ]3, 13, 3214 (1976); S. ])ESER and B. ZUMINO: Phys. Lett., 62B, 335 (1976). 581