Generalized Grassmann algebras with applications to Fermi systems
- 1 April 1980
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (4) , 601-608
- https://doi.org/10.1063/1.524504
Abstract
Generalized Grassmann numbers xi (i=1,2,⋅⋅⋅,n) are defined as those satisfying the relations xixj=ηijxjxi with ηij =−(+ or −) for i=j(i≠j). Ordinary Grassmann numbers correspond to a special case ηij=− for all i, j. Mathematical properties of such numbers are discussed in detail, and it is found that most of the results known for the ordinary case can naturally be extended to the general case. Applications are made to a description of general Fermi systems where the commutation relations belong to an arbitrary anomalous case.Keywords
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