scholarly journals Deformation quantization with minimal length

2021 ◽  
Vol 25 (1) ◽  
pp. 59-100
Author(s):  
Ziemowit Domański ◽  
Maciej Błaszak
Keyword(s):  
Deformation Quantization ◽  
Minimal Length

A Poincaré covariant noncommutative spacetime

2018 ◽  
Vol 15 (09) ◽  
pp. 1850159 ◽  
Author(s):  
Albert Much ◽  
J. David Vergara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Deformation Quantization ◽  
Deformation Theory ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Ball Problem ◽  
Noncommutative Spacetime

We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman and Mandula [All possible symmetries of the [Formula: see text] matrix, Phys. Rev. 159 (1967) 1251–1256] (see also [Much, Pottel and Sibold, Preconjugate variables in quantum field theory and their applications, Phys. Rev. D 94(6) (2016) 065007]) as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative spacetime with a minimal length that is given by the mass. By using this operator to define a noncommutative spacetime, we obtain a Poincaré invariant noncommutative spacetime and in addition solve the soccer-ball problem. Moreover, from recent progress in deformation theory we extract the idea of how to obtain, in a physical and mathematically well-defined manner, an emerging noncommutative spacetime. This is done by a strict deformation quantization known as Rieffel deformation (or warped convolutions). The result is a noncommutative spacetime combining a Snyder and a Moyal-Weyl type of noncommutativity that in addition behaves covariant under transformations of the whole Poincaré group.

Minimum space length

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Minimal Length ◽  
Space Length

We follow some logical principles to conclude there is a minimal length.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals DEFORMATION QUANTIZATION OF THE ISOTROPIC ROTATOR

1995 ◽  
Vol 10 (05) ◽  
pp. 399-407 ◽  
Author(s):  
A. STERN ◽  
I. YAKUSHIN
Keyword(s):  
Energy Spectrum ◽  
Quantum System ◽  
Chiral Symmetry ◽  
Deformation Quantization ◽  
Rigid Rotator

We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual SU (2) × SU (2) chiral symmetry, but instead [Formula: see text]. We give the energy spectrum for the resulting system.

scholarly journals Physics on the smallest scales: an introduction to minimal length phenomenology

2012 ◽  
Vol 33 (4) ◽  
pp. 853-862 ◽  
Author(s):  
Martin Sprenger ◽  
Piero Nicolini ◽  
Marcus Bleicher
Keyword(s):  
Minimal Length

Paths of Minimal Length Within Hypercubes

1966 ◽  
Vol 73 (8) ◽  
pp. 868 ◽  
Author(s):  
R. A. Jacobson
Keyword(s):  
Minimal Length
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