Related papers: Commutators, paraproducts and BMO in non-homogeneo…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
Bethe-Salpeter equation in the non-commutative space for a scalar-scalar bound state is considered. It is shown that in the non-relativistic limit, the effect of spatial non-commutativity appears as if there exist a magnetic dipole moment…
In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4-dimensional manifold, we compute this…
We sharpen in this work the tools of paracontrolled calculus in order to provide a complete analysis of the parabolic Anderson model equation and Burgers system with multiplicative noise, in a $3$-dimensional Riemannian setting, in either…
We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the…
In this contribution we discuss the Noncommutative Standard Model and the associated Standard Model-forbidden decays that can possibly serve as an experimental signature of space-time noncommutativity.
A new Lagrangian description that interpolates between the Nambu--Goto and Polyakov version of interacting strings is given. Certain essential modifications in the Poission bracket structure of this interpolating theory generates…
This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of $BMO$-type spaces. The results are formulated in a very general framework in which $BMO$ spaces are…
We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish…
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…
We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This…
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…
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our…
We consider iterated commutators of multiplication by a symbol function and tensor products of Hilbert or Riesz transforms. We establish mixed BMO classes of symbols that characterize boundedness of these objects in $L^p$. Little BMO and…
The second virial coefficient $B_{2}^{nc}(T)$ for non-interacting particles moving in a two-dimensional noncommutative space and in the presence of a uniform magnetic field $\vec B$ is presented. The noncommutativity parameter $\te$ can be…
We review the connection between noncommutative gauge theory, matrix models and fluid mechanical systems. The noncommutative Chern-Simons description of the quantum Hall effect and bosonization of collective fermion states are used as…
We give a class of Fourier multipliers with non-symmetric symbols and explicit norm bounds on $L^p$ spaces by using the stochastic calculus of L\'evy processes and Burkholder-Wang estimates for differentially subordinate martingales.
Within the framework of scenarios of nonhomogeneous baryosynthesis, the formation of macroscopic antimatter domains is predicted in a matter-antimatter asymmetrical Universe. The properties of antimatter within the domains are outlined; the…
In this paper, the authors study the matrix-valued harmonic functions and characterize them by the Poisson integral of functions in non-commutative BMO (bounded mean oscillation) spaces. This provides a very satisfactory non-commutative…