Abstract
Each isometric complex structure on a 2ℓ-dimensional euclidean space E corresponds to an identification of the Clifford algebra of E with the canonical anticommutation relation algebra for ℓ ( fermionic) degrees of freedom. The simple spinors in the terminology of E. Cartan or the pure spinors in the one of C. Chevalley are the associated vacua. The corresponding states are the Fock states (i.e. pure free states), therefore, none of the above terminologies is very good.
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References
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© 1993 Springer Science+Business Media Dordrecht
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Dubois-Violette, M. (1993). Complex Structures and the Elie Cartan Approach to the Theory of Spinors. In: Oziewicz, Z., Jancewicz, B., Borowiec, A. (eds) Spinors, Twistors, Clifford Algebras and Quantum Deformations. Fundamental Theories of Physics, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1719-7_2
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DOI: https://doi.org/10.1007/978-94-011-1719-7_2
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