2019/05/07 by Detlev Buchholz, Klaus Fredenhagen, Buchholz, Detlev +1
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1905.02711
Based on the assumption that time evolves only in one direction and\nmechanical systems can be described by Lagrangeans, a dynamical C*-algebra is\npresented for non-relativistic particles at atomic scales. Without presupposing\nany quantization scheme, this algebra is inherently non-commutative and\ncomprises a large set of dynamics. In contrast to other approaches, the\ngenerating elements of the algebra are not interpreted as observables, but as\noperations on the underlying system; they describe the impact of temporary\nperturbations caused by the surroundings. In accordance with the doctrine of\nNils Bohr, the operations carry individual names of classical significance.\nWithout stipulating from the outset their `quantization', their concrete\nimplementation in the quantum world emerges from the inherent structure of the\nalgebra. In particular, the Heisenberg commutation relations for position and\nvelocity measurements are derived from it. Interacting systems can be described\nwithin the algebraic setting by a rigorous version of the interaction picture.\nIt is shown that Hilbert space representations of the algebra lead to the\nconventional formalism of quantum mechanics, where operations on states are\ndescribed by time-ordered exponentials of interaction potentials. It is also\ndiscussed how the familiar statistical interpretation of quantum mechanics can\nbe recovered from operations.\n