# Classical/Quantum=Commutative/Noncommutative?

@article{Kisil2012ClassicalQuantumCommutativeNoncommut, title={Classical/Quantum=Commutative/Noncommutative?}, author={V. W. Kisil'}, journal={arXiv: Quantum Physics}, year={2012} }

In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires noncommutative one (q-numbers). The rest of theory can be unchanged. In this paper we critically review Dirac's proposition. We provide a natural formulation of classical mechanics through noncommutative quantities with a non-zero Planck constant. This is…

## 4 Citations

Symmetry, Geometry and Quantization with Hypercomplex Numbers

- Mathematics
- 2017

These notes describe some links between the group SL2(R), the Heisenberg group and hypercomplex numbers - complex, dual and double numbers. Relations between quantum and classical mechanics are…

Deterministic Actions on Stochastic Ensembles of Particles Can Replicate Wavelike Behaviour of Quantum Mechanics: Does It Matter?

- Physics
- 2018

A synthesis of ideas appeared from the field's founders to modern contextual approaches is proposed, which demonstrates that deterministic physical principles can replicate wavelike probabilistic effects when applied to stochastic ensembles of particles.

An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library

- MathematicsProceedings of the International Geometry Center
- 2019

A method is described, which reduces a collection of conformally in\-vari\-ant geometric relations to a system of linear equations, which may be accompanied by one fixed quadratic relation, which operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality and metrics with any signatures.

Induced Representations and Hypercomplex Numbers

- Mathematics
- 2013

In the search for hypercomplex analytic functions on the halfplane, we review the construction of induced representations of the group $${G = {\rm SL}_2(\mathbb{R})}$$ . Firstly we note that G-action…

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