Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models high energy physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate quantum such model, mechanical system spatial noncommutativity, which is inspired by works in noncommutative geometry field theory for universal...

Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions the system are obtained after model re-expressed in terms of canonical variables, performing a particular Bopp’s shift to noncommutating degrees freedom. Employing Simon’s separability criterion, we find that states entangled provided unique function (mass and frequ...

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ = ǫ k ij θk and a momentum noncommutativity matrix parameter βij = ǫ k ij βk, is showed to be equivalent to QuantumMechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformatio...

The purpose of this paper is to present an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical theory must occur in a context of noncommutative algebra and noncommutative vector analysis. In this way the formalism of quantum mechanics occurs first, but not necessarily with the usual interpretations. By...

The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality symmetries relating various noncommutative gauge models are being discussed. ∗Work supported by RFBR grant #, INTAS grant # and Scientific School Support grant #.