Related papers: Quaternions and Small Lorentz Groups in Noncommuta…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
Variables parametrized by closed and open curves are defined to reformulate compact U(1) Quantum Electrodynamics in the circle with a massless fermion field. It is found that the gauge invariant nature of these variables accommodates into a…
Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as a model of electron. It is shown that such singularities…
Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based…
An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
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…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
The quantum N-dimensional orthogonal vector Cayley-Klein spaces with different combinations of quantum structure and Cayley-Klein scheme of contractions and analytical continuations are described for multipliers, which include the first and…
To construct ternary "quaternions" following Hamilton we must introduce two "imaginary "units, $q_1$ and $q_2$ with propeties $q_1^n=1$ and $q_2^m=1$. The general is enough difficult, and we consider the $m=n=3$. This case gives us the…
We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space…
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…
We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $\Delta x=~(1-q)x$. Then, based on this, we develop the basic formalism of quantum…
The electromagnetic and axial form factors of the nucleon and its lowest positive parity excitations, the Delta(1232) and the N*(1440), are calculated with constituent-quark models that are specified by simple algebraic representations of…
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…
In this talk, recent results are presented of calculations of electromagnetic form factors of hadrons in the framework of two quantum field theories (QFT), (a) Dual-Large $N_c$ QCD (Dual-$QCD_\infty$) for the pion, proton, and…
Recently, developments in the understanding of low-energy N=1 supersymmetric gauge theory have revealed two important phenomena: the appearance of new four-dimensional superconformal field theories and a non-Abelian generalization of…
The phenomenological investigation of noncommutative space-time in the laboratory frame are presented. We formulate the apparent time variation of noncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to the earth's…
A double perturbation idea is presented in framework of the quark-gluon plasma kinetic theory. A solvable set of equations from the 'double perturbation' is derived and the equations are showed to be gauge-independent. The formalism of…