Abstract
It is well known that solutions to Dirac’s bispinor equation require an auxiliary global field of orthonormal frames on the spacetime manifold to define “spinor structure”. Constrained tensor equivalents to Dirac’s bispinor equation, which have been studied since 1937, do not require this spinor structure. We have previously shown that all tensor equivalents to the Dirac equation are produced by an extension to bispinors of Cartan’s spinor map. Here we show using the properties of this map, that spinor structure is unobservable for positive energy, square integrable solutions to the Dirac bispinor equation.
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References
R. Geroch, (1968) “Spinor Structure of Space-Times in General Relativity”, J. Math Phys. 9, page 1739.
E. Cartan, (1966) Theory of Spinors MIT, Cambridge, MA.
F. Reifler and R. Morris, “A New Formulation of the Einstein-Dirac Lagrangian”, (in review).
Y. Takahashi, (1983) “The Fierz Identities-A Passage Between Spinors and Tensors”, J. Math. Phys. 24, page 1783.
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© 1989 Springer Science+Business Media Dordrecht
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Reifler, F., Morris, R.D. (1989). The Unobservability of Spinor Structure. In: Kafatos, M. (eds) Bell’s Theorem, Quantum Theory and Conceptions of the Universe. Fundamental Theories of Physics, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0849-4_27
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DOI: https://doi.org/10.1007/978-94-017-0849-4_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4058-9
Online ISBN: 978-94-017-0849-4
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