XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Ali Mostafazadeh

Quantum system with a dynamical state space and a geometric extension of quantum mechanics

We address the problem of defining the energy observable for a quantum system whose state space depends on time. The solution leads to a moderate geometric extension of QM where the role of the Hilbert space and the Hamiltonian operator is played by a complex Hermitian vector bundle E endowed with a metric-compatible connection and a global section of a real vector bundle determined by E. The axioms of QM are not replaced by others but elevated to the level of the relevant bundles. The standard description of quantum systems in terms of a Hilbert space and a Hamiltonian operator, which respectively determine the kinematical and dynamical properties of the system, is recovered locally, i.e., in local patches of E. A major part of this work is conducted during WGMP XXXVI which was held in Białowiezia in 2017.

Reference: Phys. Rev. D 98, 046022 (2018), arXiv: 1803.04175.

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