Related papers: Noncommutative sedeons and their application in fi…
New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation…
We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential…
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…
Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that…
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity…
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into…
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the gauge…
We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial…
Using Fedosov theory of deformation quantization of endomorphism bundle we construct several models of pure geometric, deformed vacuum gravity, corresponding to arbitrary symplectic noncommutativity tensor. Deformations of Einstein-Hilbert…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$ and its unitary irreducible representations. We solve the Klein-Gordon equation in…
We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is…
We consider the relativistic phase space coordinates (x_{\mu},p_{\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time…
We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a $H$-algebra; non-commutative analogues of groups and contain the class of Voiculescu's dual groups. We are…
Tensor 50-component form of the first order relativistic wave equation for a particle with spin 2 and anomalous magnetic moment is extended to the case of an arbitrary curved space-time geometry. An additional parameter considered in the…