Abstract
From the beginning of quantum mechanics, it was assumed that an observable quantity should be represented by a self-adjoint operator in Hilbert space, the various values which could be obtained by measuring this quantity (when the system is in an eigenstate) being the (real) eigen-values of that operator and the corresponding eigenvectors being the particular states of the physical system for which these values are obtained. In the absence of the so-called superselection rules (a nontrivial operator commuting with all observables), it was also assumed that every self- adjoint operator on the Hilbert space of states corresponds to an observable.
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Flato, M., Sternheimer, D. (1980). Separate and Joint Analyticity of Vectors in Group Representations and an Application to Field Theory. In: Wolf, J.A., Cahen, M., De Wilde, M. (eds) Harmonic Analysis and Representations of Semisimple Lie Groups. Mathematical Physics and Applied Mathematics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8961-0_13
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DOI: https://doi.org/10.1007/978-94-009-8961-0_13
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