Spinor, scalar, and vector irreducible representations of generators of the Lorentz transformations in a four‐dimensional Grassmann subspace of a d‐dimensional Grassmann space are studied. For d=5 there are four spinor representations with the properties of Majorana spinors and two scalar, two three‐vector and two four‐vector representations with the properties of bosons, offering the possibility of the canonical quantization of not only bosonic but also fermionic fields.
REFERENCES
1.
F. A. Berezin and M. S. Marinov, The Methods of Second Quantization, Pure and Applied Physics (Academic, New York, 1966), Chaps. 1.3, 2.5;
A.
Barducci
, R.
Casalbuoni
, and L.
Lussanna
, Nucl. Phys. B
124
, 521
(1977
);2.
IC/91/369, IC/91/370; IJS.TP.92/4; IJS.TP.92/5; IJS.TP.92/22.
3.
C. Itzykson and J. B. Zuber, Quantum Field Theory, International Series (McGraw-Hill, New York, 1980), Chap. 2.4.
4.
L. Fonda and G. C. Ghirardi, Symmetry Principles in Quantum Physics (Marcel Dekker, New York, 1970) (Theoretical Physics), Chap. 3.
5.
L. M. Graves, The Theory of Functions of a Real Variable (McGraw-Hill, New York, 1956).
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© 1993 American Institute of Physics.
1993
American Institute of Physics
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