Quantum objects in a sheaf framework

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Fedorova, Antonina N.^1 ; Zeitlin, Michael G.^1

IPME RAS, V.O. Bolshoj pr., 61, St.-Petersburg, 199178, Russia^1

关键词: Hidden symmetry;    Infinite dimensional;    Multi-scale;    Quantum object;    Quantum phenomena;    Quantum state;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012224/pdf
DOI  :  10.1088/1742-6596/490/1/012224

来源: IOP

【 摘 要 】

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the proper category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtrations decomposed into the (entangled) orbits generated by actions/representations of internal hidden symmetries. In such a way, we open a possibility for the exact description and reinterpretation of a lot of quantum phenomena.