Related papers: The 1/N Expansion in Noncommutative Quantum Mechan…
Application of the noncommutative geometry to several physical models is considered.
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative…
The non-Abelian analog of the classical Coulomb gas is discussed. The statistical mechanics of arrays of classical particles which transform under various representations of a non-Abelian gauge group and which interact through non-Abelian…
As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
We study a parametric deformation of the unified genus-1 anharmonic potential and derive a parametric form of perturbative/nonperturbative (P/NP) relation, applicable across all parameter values. We explicitly demonstrate that the…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no…
We discuss non perturbative corrections to the Coulomb-like potential of heavy quarks at short distances. We consider both the standard framework provided by infrared renormalons and the assumption that confinement does not allow weak…
We discuss certain generalization of the Hilbert space of states in noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can…
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces $\DC P^N$, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
Perturbative corrections to N=1/2 supersymmetric U(N) gauge theory at one-loop order are studied. It is shown that whereas the quantum corrections to N=1 sector of the theory are not affected by the C-deformation, the non(anti)commutativity…
We consider a model of non-commutative Quantum Mechanics given by two harmonic oscillators over a non-commutative two dimensional configuration space. We study possible ways of removing the non-commutativity based on the classical limit…
We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency $\Omega$ is chosen to scale with the order as…
We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the "growth" of certain operator spaces: It implies asymptotically…