Deformation quantization with minimal length

Domański, Ziemowit; Błaszak, Maciej; ski, Ziemowit Doma; B aszak, Maciej

doi:10.4310/atmp.2021.v25.n1.a2

Advances in Theoretical and Mathematical Physics

2021

DOI: 10.4310/atmp.2021.v25.n1.a2

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Deformation quantization with minimal length

Ziemowit Domański

Maciej Błaszak

Ziemowit Doma ski

et al.

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2024

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Minimal length scale in quantum mechanics from a deformation quantization perspective

Domański

2024

J. Phys.: Conf. Ser.

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We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.

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Minimal length scale in quantum mechanics from a deformation quantization perspective

Domański

2024

J. Phys.: Conf. Ser.

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Deformation quantization with minimal length

Cited by 1 publication

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Minimal length scale in quantum mechanics from a deformation quantization perspective

Minimal length scale in quantum mechanics from a deformation quantization perspective

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