Related papers: Time-Space Noncommutativity And Symmetries For A M…
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard…
We discuss various symmetry properties of the reparametrization invariant toy model of a free non-relativistic particle and show that its commutativity and noncommutativity (NC) properties are the artifact of the underlying symmetry…
We study space-time symmetries in Non-Commutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in \cite{sg}, has been considered. Subtle features of Lorentz invariance…
We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge,…
We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our…
Any effort to localise an event in the vicinity of the Planck length scale, only where the quantum gravitational effects are predicted to be observed, will invariably result in gravitational collapse. One must postulate noncommutative (NC)…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
I discuss the indefinite metrical structure of the time-space translations as realized in the indefinite inner products for relativistic quantum fields, familiar in the example of quantum gauge fields. The arising indefinite unitary…
Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…
In this work I show by a first principles calculation that quantum states describing massive relativistic free spinning particles obey kinematical conditions whose origin can be traced to parity as a good quantum number. These conditions…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
In this work, we will analyze a noncommutative (NC) version of the Friedmann-Robert-Walker cosmological models within the gravitational Ho\v{r}ava-Lifshitz theory. The matter content of the models is described by a perfect fluid and the…
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates.…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
We study a classical, noncommutative (NC), Friedmann-Robertson-Walker cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial…
We study the space-time invariances of the bosonic relativistic particle and bosonic relativistic string using general formulations obtained by incorporating the Hamiltonian constraints into the formalism. We point out that massless…
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],…