Heisenberg algebra

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Heisenberg algebra

[′hīz·ən·bərg ‚al·jə·brə]
(quantum mechanics)
The Lie algebra formed by the operators of position and momentum.
References in periodicals archive ?
He describes Lie groups and their representations, with a focus on the quantum mechanically relevant Heisenberg group H3 and special unitary group SU(2).
New methods for constructing a canal surface surrounding a biharmonic curve in the Lorentzian Heisenberg group [Heis.
Roughly put (see the citation [15] for more details), if for an STGQ ([GAMMA], x, E), E is isomorphic to a general Heisenberg group, then [GAMMA] is a flock quadrangle:
We will be interested in deformations of the discrete Heisenberg group as a group acting properly discontinuously and cocompactly on a space X.
But many groups in physics such as the Heisenberg group and also many applicable groups in engineering such as Motion groups are non-abelian and so that the standard STFT theory in abelian case fails.
Thanks to the magic (and obvious) relation between the 2n + 1-dimensional Heisenberg group and its vector group [R.
In this paper we describe a method to derive a Weierstrass-type representation formula for simply connected immersed minimal surfaces in Heisenberg group [H.
Turhan: Completeness of Lorentz Metric on 3-Dimensional Heisenberg Group, Int.
Hans-Jurgen Eisler, who heads the DFG Heisenberg group at the Light Technology Institute.
Ten chapters discuss the skew field of quaternions; elements of the geometry of S3, Hopf bundles, and spin representations; internal variables of singularity free vector fields in a Euclidean space; isomorphism classes, Chern classes, and homotopy classes of singularity free vector fields in 3-space; Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras, and special linear groups; the Heisenbreg group and natural C*-algebras of a vector field in 3-space; the Schrodinger representation and the metaplectic representation; the Heisenberg group as a basic geometric background of signal analysis and geometric optics; quantization of quadratic polynomials; and field theoretic Weyl quantization of a vector field in 3-space.
This Heisenberg group has many important applications on Sub-Riemannian geometry and has very important role in physics.
Analysis of the Hodge Laplacian on the Heisenberg Group