Showing papers on "Quantum geometry published in 1967"
TL;DR: In this paper, the eigenvalues of finite translations are used for specifying a complete set of states in quantum mechanics and a derivation of these states is given and they are shown to be very useful in solid-state physics.
Abstract: Eigenvalues of finite translations are used for specifying a complete set of states in quantum mechanics. A derivation of these states is given and they are shown to be very useful in solid-state physics.
274 citations
TL;DR: In this paper, a generalization of the current interpretation of quantum mechanics is proposed that would also include the case of incompatible observables, by taking advantage of the concept of complex probability measure.
Abstract: The empirical meaning of the simultaneity of measurement of several observables is carefully analyzed. General criteria sufficient to guarantee the internal consistency of a framework including simultaneous measurements of incompatible observables are put forward. The case is illustrated with the example of simultaneous measurements of position and momenta of particles in quantum mechanics. It is pointed out that, in general, the outcome of measurements of incompatible observables cannot be described statistically by means of the probability measures of mathematical statistics, which have primarily been introduced only with compatible observables in mind. The concept of complex probability measure is put forward. A generalization of the current interpretation of quantum mechanics is proposed that would also include the case of incompatible observables, by taking advantage of the concept of complex probability measure.
41 citations
39 citations
30 citations
TL;DR: In this article, a complete system of observables and superselection rules are considered in an axiomatic framework for quantum mechanics which generalizes the usual Hilbert space formulation, and it is shown that many of the Hilbert space theorems carry over to this abstract formalism.
Abstract: Systems of observables are considered in an axiomatic framework for quantum mechanics which generalizes the usual Hilbert space formulation. Familiar concepts such as complete systems of observables and superselection rules are generalized and it is shown that many of the Hilbert space theorems carry over to this abstract formalism. Also functions of observables are considered and some theorems due to John von Neumann are generalized.
9 citations
TL;DR: In this paper, it was shown that the energy-momentum spectrum of a quantum field cannot be bounded under special assumptions, assuming Einstein causality, and it was proved that the result holds for all quantum fields.
Abstract: It is proved, assuming Einstein causality, that the energy-momentum spectrum of a quantum field cannot be bounded. More is known under special assumptions [1, 4]. Our main concern is the method and general applicability of the result.
8 citations
5 citations
1 citations