Twist deformation of l-conformal Galilei Hopf algebra
The six Abelian twist-deformations of l-conformal Galilei Hopf algebra are considered. The corresponding twisted space-times are derived as well.
hep-th↗
arXiv subjects
Marcin Daszkiewicz
Publications and source records attributed to Marcin Daszkiewicz.
Quantum mechanics of many particles defined on twisted N-enlarged Newton-Hooke space-times
We provide the quantum mechanics of many particles moving in twisted N-enlarged Newton-Hooke space-time. In particular, we consider the example of such noncommutative system - the set of M particles moving in Coulomb field of external point-like source and interacting each other also by Coulomb potential.
hep-th↗
Landau energy levels for twisted N-enlarged Newton-Hooke space-time
We derive the Landau energy levels for twisted N-enlarged Newton-Hooke space-time, i.e. we find the time-dependent energy spectrum and the corresponding eigenstates for an electron moving in uniform magnetic as well as in uniform electric external fields.
hep-th↗
Generalized twist-deformed Rindler space-times
The (linearized) quantum Rindler space-times associated with generalized twist-deformed Minkowski spaces are provided. The corresponding corrections to the Hawking spectra linear in deformation parameters are derived.
math-ph↗
Generating of additional force terms in Newton equation by twist-deformed Hopf algebras and classical symmetries
We compare two ways of force terms generating in the model of nonrelativistic particle moving in the presence of constant field force $\vec{F}$. First of them uses the twist-deformed acceleration-enlarged Newton-Hooke quantum space-times while the second one incorporates the doubly enlarged Newton-Hooke transformations of classical space. Particulary, we find the conditions for which the both treatments provide the same force terms.
math-ph↗
N-enlarged Galilei Hopf algebra and its twist deformations
The N-enlarged Galilei Hopf algebra is constructed. Its twist deformations are considered and the corresponding twisted space-times are derived.
math-ph↗
Twist deformation of doubly enlarged Newton-Hooke Hopf algebra
We provide fifteen twist-deformed doubly enlarged Newton-Hooke quantum space-times. In $τ$ approaching infinity limit the twisted doubly enlarged Galilei spaces are obtained as well.
math-ph↗
Twisted acceleration-enlarged Newton-Hooke space-times and breaking classical symmetry phenomena
We find the subgroup of classical acceleration-enlarged Newton-Hooke Hopf algebra which acts covariantly on the twisted acceleration-enlarged Newton-Hooke space-times. The case of classical acceleration-enlarged Galilei quantum group is considered as well.
math-ph↗
Saturation of uncertainty relations for twisted acceleration-enlarged Newton-Hooke space-times
Using Fock representation we construct states saturating uncertainty relations for twist-deformed acceleration-enlarged Newton-Hooke space-times.
math-ph↗
Twisted acceleration-enlarged Newton-Hooke space-times and conservative force terms
There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that only in the case of canonical twist deformation the force terms generated by space-time noncommutativity remain conservative for both models.
math-ph↗
Classical mechanics of many particles defined on canonically deformed nonrelativistic space-time
We provide the classical mechanics of many particles moving in canonically twist-deformed space-time. In particular, we consider two examples of such noncommutative systems - the set of N particles moving in gravitational field as well as the system of N interacting harmonic oscillators.
hep-th↗
Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-times
The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke space-times are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time.
math-ph↗
Twisted acceleration-enlarged Newton-Hooke Hopf algebras
Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrate that their contraction limit $τ\to \infty$ leads to the new twisted acceleration-enlarged Galilei spaces.
math-ph↗
Deformation of nonrelativistic space-time and forces noticed by noninertial observer
We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph], we recall that the considered noncommutativity generates additional force terms, which appear in the corresponding Newton equation. We demonstrate that the same force terms can be generated by the proper noninertial transformation of classical nonrelativistic space-time.
math-ph↗
Twisted Rindler space-times
The (linearized) noncommutative Rindler space-times associated with canonical, Lie-algebraic and quadratic twist-deformed Minkowski spaces are provided. The corresponding deformed Hawking spectra detected by Rindler observers are derived as well.
math-ph↗
Phase spaces of twisted Lie-algebraically deformed relativistic and nonrelativistic symmetries
The twisted Lie-algebraically deformed relativistic and nonrelativistic phase spaces are constructed with the use of Heisenberg double procedure. The corresponding Heisenberg uncertainty principles are discussed as well.
math-ph↗
Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.
hep-th↗
Twist deformations of Newton-Hooke Hopf algebras
We construct five new quantum Newton-Hooke Hopf algebras with the use of Abelian twist procedure. Further we demonstrate that the corresponding deformed space-times with quantum space and classical time are periodic or expanding in time.
hep-th↗