The Transformation of Commutative Phase Space to Noncommutative One, and its Lorentz Transformation-Like Forms

2021 ◽  
pp. 188-198
Author(s):  
Makoto Nakamura ◽  
Hiroshi Kakuhata ◽  
Kouichi Toda
Keyword(s):  
Phase Space ◽  
Lorentz Transformation ◽  
Linear Transformation ◽  
Arbitrary Dimension ◽  
Two Dimensional ◽  
Exact Form ◽  
Noncommutative Phase Space ◽  
Two Dimension ◽  
Direct Sum

Noncommutative phase space of arbitrary dimension is discussed. We introduce momentum-momentum noncommutativity in addition to co-ordinate-coordinate noncommutativity. We find an exact form for the linear transformation which relates a noncommutative phase space to the corresponding ordinary one. By using this form, we show that a noncommutative phase space of arbitrary dimension can be represented by the direct sum of two-dimensional noncommutative ones. In two-dimension, we obtain the transformation which relates a noncommutative phase space to commutative one. The transformation has the Lorentz transformation-like forms and can also describe the Bopp's shift.

ENTANGLED STATE REPRESENTATIONS IN NONCOMMUTATIVE PHASE SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4685-4693
Author(s):  
GUANG-JIE GUO ◽  
CHAO-YUN LONG ◽  
SHUI-JIE QIN ◽  
ZHENG-REN ZHANG ◽  
HUA-XIONG CHEN
Keyword(s):  
Energy Spectrum ◽  
Phase Space ◽  
Harmonic Oscillator ◽  
Entangled State ◽  
Two Dimensional ◽  
Entangled State Representation ◽  
State Representation ◽  
Noncommutative Phase Space

The entangled state representation has been constructed on noncommutative phase space. Using this appropriate representation, the energy spectrum of general two-dimensional harmonic oscillator has been obtained exactly.

scholarly journals Decoherence of a Damped Anisotropic Harmonic Oscillator under Magnetic Field Effects in a Two-Dimensional Noncommutative Phase-Space

2020 ◽  
Vol 08 (12) ◽  
pp. 2801-2823
Author(s):  
Martin Tcoffo ◽  
Germain Yinde Deuto ◽  
Issofa Nsangou ◽  
Armel Azangue Koumetio ◽  
Lylyane S. Yonya Tchapda ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Magnetic Field Effects ◽  
Noncommutative Phase Space ◽  
Field Effects

scholarly journals Noncommutative Phase Space Schrödinger Equation with Minimal Length

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
Z. Molaee ◽  
S. Zarrinkamar
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
External Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Minimal Length ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues

We consider the Schrödinger equation under an external magnetic field in two-dimensional noncommutative phase space with an explicit minimal length relation. The eigenfunctions are reported in terms of the Jacobi polynomials, and the explicit form of energy eigenvalues is reported.

scholarly journals Two-Dimensional Pauli Equation in Noncommutative Phase-Space

2021 ◽  
Vol 66 (9) ◽  
pp. 771
Author(s):  
I. Haouam
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Classical Limit ◽  
Helmholtz Free Energy ◽  
Particle Systems ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Pauli Equation ◽  
The Impact ◽  
Space Noncommutativity

We study the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. The noncommutative problem is related to the equivalent commutative one through a set of two-dimensional Bopp-shift transformations. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. In the classical limit, we have derived the noncommutative semiclassical partition function for one- and N- particle systems. The thermodynamic properties such as the Helmholtz free energy, mean energy, specific heat and entropy in noncommutative and commutative phasespaces are determined. The impact of the phase-space noncommutativity on the Pauli system is successfully examined.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Regular Hom-algebras admitting a multiplicative basis

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio J. Calderón Martín
Keyword(s):  
Arbitrary Dimension ◽  
Base Field ◽  
Direct Sum ◽  
Multiplicative Basis ◽  
Arbitrary Base ◽  
The Family

AbstractLet {({\mathfrak{H}},\mu,\alpha)} be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field {{\mathbb{F}}}. A basis {{\mathcal{B}}=\{e_{i}\}_{i\in I}} of {{\mathfrak{H}}} is called multiplicative if for any {i,j\in I}, we have that {\mu(e_{i},e_{j})\in{\mathbb{F}}e_{k}} and {\alpha(e_{i})\in{\mathbb{F}}e_{p}} for some {k,p\in I}. We show that if {{\mathfrak{H}}} admits a multiplicative basis, then it decomposes as the direct sum {{\mathfrak{H}}=\bigoplus_{r}{{\mathfrak{I}}}_{r}} of well-described ideals admitting each one a multiplicative basis. Also, the minimality of {{\mathfrak{H}}} is characterized in terms of the multiplicative basis and it is shown that, in case {{\mathcal{B}}}, in addition, it is a basis of division, then the above direct sum is composed by means of the family of its minimal ideals, each one admitting a multiplicative basis of division.

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