1 5 Ju n 20 09 Position - dependent noncommutativity in quantum mechanics
نویسندگان
چکیده
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinatesˆx i , ˆ x j = ω ij (ˆ x), and construct the complete algebra of commutation relations, including the operators of mo-menta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativety.
منابع مشابه
ar X iv : h ep - t h / 04 07 24 7 v 1 2 8 Ju l 2 00 4 N = 2 SUPERSYMMETRIC PLANAR PARTICLES AND MAGNETIC INTERACTION FROM NONCOMMUTATIVITY
We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N = 2 superfield technique and show that in the presence of a scalar N = 2 superpotential the magnetic interaction is implied by the presence of noncommutativity of position vari...
متن کاملar X iv : h ep - t h / 05 01 23 1 v 1 2 8 Ja n 20 05 Noncommutative Quantum Mechanics with Path Integral ∗
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative r...
متن کامل0 50 20 03 v 2 1 3 Ju n 20 05 Noncommutative Configuration Space . Classical and Quantum Mechanical Aspects ∗
In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates {q i , p k } the canonical symplectic two-form is ω 0 = dq i ∧ dp i. It is well known in symplectic mechanics [5, 6, 9] that the interaction of a charged particle with a magnetic field can be described in a Hamil-tonian formalism without a choice of a potential...
متن کاملar X iv : 0 81 1 . 40 90 v 3 [ m at h . Q A ] 2 3 Ju n 20 09 MODULE CATEGORIES OVER POINTED HOPF ALGEBRAS
We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).
متن کاملTest of Quantum Effects of Spatial Noncommutativity using Modified Electron Momentum Spectroscopy
The possibility of testing spatial noncommutativity by current experiments on normal quantum scales is investigated. For the case of both position-position and momentum-momentum noncommuting spectra of ions in crossed electric and magnetic fields are studied in the formalism of noncommutative quantum mechanics. In a limit of the kinetic energy approaching its lowest eigenvalue this system posse...
متن کامل