Quantum points/patterns, Part 1: from geometrical points to quantum points in a sheaf framework

Antonina N. Fedorova; Michael G. Zeitlin

doi:10.1117/12.893502

28 September 2011 Quantum points/patterns, Part 1: from geometrical points to quantum points in a sheaf framework

Antonina N. Fedorova, Michael G. Zeitlin

Proceedings Volume 8121, The Nature of Light: What are Photons? IV; 81210J (2011) https://doi.org/10.1117/12.893502
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtration. Three different symmetries, kinematical (on space-time), hidden/dynamical (on sections of sheaves), unified (on filtration of the full scale of spaces) are generic objects generating the full zoo of quantum phenomena.

Citation Download Citation

Antonina N. Fedorova and Michael G. Zeitlin "Quantum points/patterns, Part 1: from geometrical points to quantum points in a sheaf framework", Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 81210J (28 September 2011); https://doi.org/10.1117/12.893502

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